Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We...Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.展开更多
In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the ...In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the free boundaries.展开更多
In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO（μ） functions on non-homogeneous metric measure spaces is obtained.
Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0<p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈∈(0,∞).In this paper,the authors introduce the ato...Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0<p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈∈(0,∞).In this paper,the authors introduce the atomic Hardy space Hp,q,γ atb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ∈(μ)via the discrete coefficient K(ρ),p B,S,and prove that the Calder′on-Zygmund operator is bounded from Hp,q,γ,δmb,ρ(μ)(or Hp,q,γatb,ρ(μ))into Lp(μ),and from Hp,q,γ+1atb,ρ(ρ+1)(μ)into H p,q,γ,12(δ-νp+ν)mb,ρ(μ).The boundedness of the generalized fractional integral Tβ(β∈(0,1))from Hp1,q,γ,θmb,ρ(μ)(or Hp1,q,γatb,ρ(μ))into Lp2(μ)with 1/p2=1/p1-β is also established.The authors also introduce theρ-weakly doubling condition,withρ∈(1,∞),of the measure and construct a non-doubling measure satisfying this condition.If isρ-weakly doubling,the authors further introduce the Campanato space Eα,qρ,η,γ(μ)and show that Eα,qρ,η,γ(μ)is independent of the choices ofρ,η,γand q;the authors then introduce the atomic Hardy space Hp,q,γatb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ(μ),which coincide with each other;the authors finally prove that Hp,q,γatb,ρ(μ)is the predual of E1/p-1,1ρ,ρ,1(μ).Moreover,if is doubling,the authors show that Eα,qρ,η,γ(μ)and the Lipschitz space Lipα,q(μ)(q∈[1,∞)),or Hp,q,γatb,ρ(μ)and the atomic Hardy space Hp,q at(μ)(q∈(1,∞])of Coifman and Weiss coincide.Finally,if(X,d,)is an RD-space(reverse doubling space)with(X)=∞,the authors prove that Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ)and Hp,q at(μ)coincide for any q∈(1,2].In particular,when(X,d,):=(RD,||,dx)with dx being the D-dimensional Lebesgue measure,the authors show that spaces Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ),Hp,q,γatb,ρ(μ)and Hp,q,γ,mb,ρ(μ)all coincide with Hp(RD)for any q∈(1,∞).展开更多
Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-...Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and b:=(b1,..., bm) be a finite family of RBMO(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator T∏bgenerated by T and b are obtained.展开更多
Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of ...Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of equations of elliptic operators in weighted divergence form{LA,φu+α▽(divu)-▽φdivu]=-su,inΩ,u∣aΩ=0,where LA,φ=div(A▽(·))-(A▽φ,▽(·)),α is a nonnegative constant and u is a vector-valued function.Some universal inequalities for eigenvalues of this problem are established.Moreover,as applications of these results,we give some estimates for the upper bound of sk+1 and the gap of sk+1-sk in terms of the first k eigenvalues.Our results contain some results for the Lam′e system and a system of equations of the drifting Laplacian.展开更多
The main goal of this paper is to establish the boundedness of bilinear strongly singular operator T^(-)and its commutator Tb_(1),b_(2)on generalized Morrey spaces M_(p)^(u)(μ)over non-homogeneous metric measure spac...The main goal of this paper is to establish the boundedness of bilinear strongly singular operator T^(-)and its commutator Tb_(1),b_(2)on generalized Morrey spaces M_(p)^(u)(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to W_(τ)forτ∈(0,2),and u1u2=u.The authors prove that T_(-)is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ),where 1/p=1/p_(1)+1/p_(2)with 1<p1,p2<∞;and also bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into generalized weak Morrey spaces WM_(p)^(u)(μ).Furthermore,the author also show that commutator Tb1,b2 generated by b_(1),b_(2)∈RBMO(μ)and T is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ).展开更多
Let(X,d,μ)be a metric measure space with non-negative Ricci curvature.This paper is concerned with the boundary behavior of harmonic function on the(open)upper half-space X×R_(+).We derive that a function f of b...Let(X,d,μ)be a metric measure space with non-negative Ricci curvature.This paper is concerned with the boundary behavior of harmonic function on the(open)upper half-space X×R_(+).We derive that a function f of bounded mean oscillation(BMO)is the trace of harmonic function u(x,t)on X×R_(+),u(x,0)=f(x),whenever u satisfies the following Carleson measure condition supx_(B),r_(B) ∫_(0)^(r_(B) ) f_(B(x_(B),r_(B))) |t■u(x,t)|^(2)dμ(x)dt/t≤C<∞,where ■=(■_(x),■_(t))denotes the total gradient and B(x_(B),r_(B)) denotes the(open)ball centered at x_(B) with radius r_(B).Conversely,the above condition characterizes all the harmonic functions whose traces are in BMO space.展开更多
Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Litt...Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.展开更多
In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the a...In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the authors first obtain the two-weight weak-type estimate for the locala fractional maximal operators of orderαfrom L^(p)(v)to L^(q,∞)(u)with 1≤p≤q<∞under a condition of(u,v)∈∪b>a A_(p,q,a)^(b') ,and then obtain the two-weight weak-type estimate for the local fractional integrals.In addition,the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of(u,v)∈M_(p,q,a)^(6a+9√da^2) and the two-weight strong-type boundedness of the local fractional integrals.These estimates are established by the radialization method and dyadic approach.展开更多
Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponen...Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponent.In this paper,we mainly study two things,one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2.The other is to study the generalized Moser-Trudinger inequality with a singular Weight.展开更多
We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 20...We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 2013, 43： 153-160].展开更多
Let(X,d,μ)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M_(b)^(α)formed by b∈RBMO(...Let(X,d,μ)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M_(b)^(α)formed by b∈RBMO(μ)and the fractional maximal function M^((α))is bounded from Lebesgue spaces L^(p)(μ)into spaces L^(q)(μ),where 1/q=1/p-αforα∈(0,1)and p∈(1,1/α).Furthermore,the boundedness of the M_(b)^(α)on Orlicz spaces L^Φ(μ)is established.展开更多
This paper presents a coordinated target localization method for clustered space robot.According to the different measuring capabilities of cluster members,the master-slave coordinated relative navigation strategy for...This paper presents a coordinated target localization method for clustered space robot.According to the different measuring capabilities of cluster members,the master-slave coordinated relative navigation strategy for target localization with respect to slavery space robots is proposed;then the basic mathematical models,including coordinated relative measurement model and cluster centralized dynamics,are established respectively.By employing the linear Kalman flter theorem,the centralized estimator based on truth measurements is developed and analyzed frstly,and with an intention to inhabit the initial uncertainties related to target localization,the globally stabilized estimator is designed through introduction of pseudo measurements.Furthermore,the observability and controllability of stochastic system are also analyzed to qualitatively evaluate the convergence performance of pseudo measurement estimator.Finally,on-orbit target approaching scenario is simulated by using semi-physical simulation system,which is used to verify the convergence performance of proposed estimator.During the simulation,both the known and unknown maneuvering acceleration cases are considered to demonstrate the robustness of coordinated localization strategy.展开更多
Surface potential decay of polymers for electrical insulation can help to determine the dark conductivity for spacecraft charging analysis. Due to the existence of radiation-induced conductivity, it decays fast in the...Surface potential decay of polymers for electrical insulation can help to determine the dark conductivity for spacecraft charging analysis. Due to the existence of radiation-induced conductivity, it decays fast in the first few hours after irradiation and exponentially slowly for the remaining time. The measurement of dark conductivity with this method usually takes the slow part and needs a couple of days. Integrating the Fowler formula into the deep dielectric charging equations, we obtain a new expression for the fast decay part. The experimental data of different materials, dose rates and temperatures are fitted by the new expression. Both the dark conductivity and the radiation-induced conductivity are derived and compared with other methods. The result shows a good estimation of dark conductivity and radiation-induced conductivity in high-resistivity polymers, which enables a fast measurement of dielectric conductivity within about 600 rain after irradiation.展开更多
This paper give some sufficient condition on the nonlinear cross section to insure thewell-posedness and asymptotic behavior of a class of time-dependent neutron transport equations inspaces of measures.
In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation re...In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.展开更多
It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb...It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).展开更多
The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)...The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_(γ)]is compact from Morrey space M_(q)^(p)(μ)into Morrey space M_(t)^(s)(μ)if and only if b∈Lip_(β)(μ).展开更多
There exists an increasing need for Milli-Arc-Seconds(MAS)accuracy pointing measurement for current and future space systems.To meet the 0.1″space pointing measurement accuracy requirements of spacecraft in future,th...There exists an increasing need for Milli-Arc-Seconds(MAS)accuracy pointing measurement for current and future space systems.To meet the 0.1″space pointing measurement accuracy requirements of spacecraft in future,the influence of spacecraft micro-vibration on a 0.1″Space Pointing Measuring Instrument(SPMI)is studied.A Quasi-Zero Stiffness Device(QZSD)with adaptive adjustment and variable stroke was proposed.Then,a series of micro-vibration experiments of the SPMI were carried out.The influence of the micro-vibration generated by Guidance Navigation Control(GNC)attitude control components under different attitudes on the SPMI was analyzed.Point spread function of image motion in micro-vibration was also derived.Further,the changes of image motion under the micro-vibration environment were evaluated by extracting the gray centroid of the images,and the experiment processes and results are deeply discussed.The results show that the firstorder frequency of the QZSD system is 0.114 Hz,and it is induced by a double pendulum system;the image motion of single flywheel spinning reached 0.015 pixels;whilst the image motion reached 0.03 pixels when three flywheels are combined spinning.These latest findings provide a beneficial theoretical and technical support for the development of spacecraft with 0·1″pointing accuracy.展开更多
基金The Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province.
文摘Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.
基金supported by the National Key R&Dprogram of China(2021YFA1003001)。
文摘In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the free boundaries.
基金supported by NSF of Anhui Province(No.1608085QA12)NSF of Education Committee of Anhui Province(Nos.KJ2016A506 and KJ2017A454)+2 种基金Excellent Young Talents Foundation of Anhui Province(No.GXYQ2017070)Doctoral Scientific Research Foundation of Chaohu University(No.KYQD-201605)Scientific Research Project of Chaohu University(No.XLY-201501)
文摘In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO（μ） functions on non-homogeneous metric measure spaces is obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11301534,11171027,11361020 and 11101339)Da Bei Nong Education Fund(Grant No.1101-2413002)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2012LYB26,2012CXQT09,2013YB60 and 2014KJJCA10)
文摘Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0<p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈∈(0,∞).In this paper,the authors introduce the atomic Hardy space Hp,q,γ atb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ∈(μ)via the discrete coefficient K(ρ),p B,S,and prove that the Calder′on-Zygmund operator is bounded from Hp,q,γ,δmb,ρ(μ)(or Hp,q,γatb,ρ(μ))into Lp(μ),and from Hp,q,γ+1atb,ρ(ρ+1)(μ)into H p,q,γ,12(δ-νp+ν)mb,ρ(μ).The boundedness of the generalized fractional integral Tβ(β∈(0,1))from Hp1,q,γ,θmb,ρ(μ)(or Hp1,q,γatb,ρ(μ))into Lp2(μ)with 1/p2=1/p1-β is also established.The authors also introduce theρ-weakly doubling condition,withρ∈(1,∞),of the measure and construct a non-doubling measure satisfying this condition.If isρ-weakly doubling,the authors further introduce the Campanato space Eα,qρ,η,γ(μ)and show that Eα,qρ,η,γ(μ)is independent of the choices ofρ,η,γand q;the authors then introduce the atomic Hardy space Hp,q,γatb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ(μ),which coincide with each other;the authors finally prove that Hp,q,γatb,ρ(μ)is the predual of E1/p-1,1ρ,ρ,1(μ).Moreover,if is doubling,the authors show that Eα,qρ,η,γ(μ)and the Lipschitz space Lipα,q(μ)(q∈[1,∞)),or Hp,q,γatb,ρ(μ)and the atomic Hardy space Hp,q at(μ)(q∈(1,∞])of Coifman and Weiss coincide.Finally,if(X,d,)is an RD-space(reverse doubling space)with(X)=∞,the authors prove that Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ)and Hp,q at(μ)coincide for any q∈(1,2].In particular,when(X,d,):=(RD,||,dx)with dx being the D-dimensional Lebesgue measure,the authors show that spaces Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ),Hp,q,γatb,ρ(μ)and Hp,q,γ,mb,ρ(μ)all coincide with Hp(RD)for any q∈(1,∞).
基金supported by National Natural Science Foundation of China(Grant Nos.11301534 and 11571039)。
文摘Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and b:=(b1,..., bm) be a finite family of RBMO(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator T∏bgenerated by T and b are obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.1100113011571361 and 11831005)the Fundamental Research Funds for the Central Universities(Grant No.30917011335)。
文摘Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of equations of elliptic operators in weighted divergence form{LA,φu+α▽(divu)-▽φdivu]=-su,inΩ,u∣aΩ=0,where LA,φ=div(A▽(·))-(A▽φ,▽(·)),α is a nonnegative constant and u is a vector-valued function.Some universal inequalities for eigenvalues of this problem are established.Moreover,as applications of these results,we give some estimates for the upper bound of sk+1 and the gap of sk+1-sk in terms of the first k eigenvalues.Our results contain some results for the Lam′e system and a system of equations of the drifting Laplacian.
基金Supported by the National Natural Science Foundation of China(Grant No.12201500)the Science Foundation for Youths of Gansu Province(Grant No.22JR5RA173)the Young Teachers’Scientific Research Ability Promotion Project of Northwest Normal University(Grant No.NWNU-LKQN2020-07)。
文摘The main goal of this paper is to establish the boundedness of bilinear strongly singular operator T^(-)and its commutator Tb_(1),b_(2)on generalized Morrey spaces M_(p)^(u)(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to W_(τ)forτ∈(0,2),and u1u2=u.The authors prove that T_(-)is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ),where 1/p=1/p_(1)+1/p_(2)with 1<p1,p2<∞;and also bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into generalized weak Morrey spaces WM_(p)^(u)(μ).Furthermore,the author also show that commutator Tb1,b2 generated by b_(1),b_(2)∈RBMO(μ)and T is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ).
文摘Let(X,d,μ)be a metric measure space with non-negative Ricci curvature.This paper is concerned with the boundary behavior of harmonic function on the(open)upper half-space X×R_(+).We derive that a function f of bounded mean oscillation(BMO)is the trace of harmonic function u(x,t)on X×R_(+),u(x,0)=f(x),whenever u satisfies the following Carleson measure condition supx_(B),r_(B) ∫_(0)^(r_(B) ) f_(B(x_(B),r_(B))) |t■u(x,t)|^(2)dμ(x)dt/t≤C<∞,where ■=(■_(x),■_(t))denotes the total gradient and B(x_(B),r_(B)) denotes the(open)ball centered at x_(B) with radius r_(B).Conversely,the above condition characterizes all the harmonic functions whose traces are in BMO space.
基金Supported by National Natural Science Foundation of China(Grant No.11471040)the Fundamental Research Funds for the Central Universities(Grant No.2014KJJCA10)
文摘Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.
基金Supported by National Natural Science Foundation of China(Grant Nos.11871452 and 12071473)Beijing Information Science and Technology University Foundation(Grant Nos.2025031)。
文摘In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the authors first obtain the two-weight weak-type estimate for the locala fractional maximal operators of orderαfrom L^(p)(v)to L^(q,∞)(u)with 1≤p≤q<∞under a condition of(u,v)∈∪b>a A_(p,q,a)^(b') ,and then obtain the two-weight weak-type estimate for the local fractional integrals.In addition,the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of(u,v)∈M_(p,q,a)^(6a+9√da^2) and the two-weight strong-type boundedness of the local fractional integrals.These estimates are established by the radialization method and dyadic approach.
文摘Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponent.In this paper,we mainly study two things,one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2.The other is to study the generalized Moser-Trudinger inequality with a singular Weight.
文摘We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 2013, 43： 153-160].
基金the Science Foundation for Youths of Gansu Province(Grant No.22JR5RA173)Master Foundation of Northwest Normal University(Grant No.2022KYZZ-S121).
文摘Let(X,d,μ)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M_(b)^(α)formed by b∈RBMO(μ)and the fractional maximal function M^((α))is bounded from Lebesgue spaces L^(p)(μ)into spaces L^(q)(μ),where 1/q=1/p-αforα∈(0,1)and p∈(1,1/α).Furthermore,the boundedness of the M_(b)^(α)on Orlicz spaces L^Φ(μ)is established.
基金supported by the National Natural Science Foundation of China (No.11102018)
文摘This paper presents a coordinated target localization method for clustered space robot.According to the different measuring capabilities of cluster members,the master-slave coordinated relative navigation strategy for target localization with respect to slavery space robots is proposed;then the basic mathematical models,including coordinated relative measurement model and cluster centralized dynamics,are established respectively.By employing the linear Kalman flter theorem,the centralized estimator based on truth measurements is developed and analyzed frstly,and with an intention to inhabit the initial uncertainties related to target localization,the globally stabilized estimator is designed through introduction of pseudo measurements.Furthermore,the observability and controllability of stochastic system are also analyzed to qualitatively evaluate the convergence performance of pseudo measurement estimator.Finally,on-orbit target approaching scenario is simulated by using semi-physical simulation system,which is used to verify the convergence performance of proposed estimator.During the simulation,both the known and unknown maneuvering acceleration cases are considered to demonstrate the robustness of coordinated localization strategy.
基金Supported by the Fundamental Research Funds for the Central Universities in Nanjing University of Aeronautics and Astronautics under Grant No NS2014089
文摘Surface potential decay of polymers for electrical insulation can help to determine the dark conductivity for spacecraft charging analysis. Due to the existence of radiation-induced conductivity, it decays fast in the first few hours after irradiation and exponentially slowly for the remaining time. The measurement of dark conductivity with this method usually takes the slow part and needs a couple of days. Integrating the Fowler formula into the deep dielectric charging equations, we obtain a new expression for the fast decay part. The experimental data of different materials, dose rates and temperatures are fitted by the new expression. Both the dark conductivity and the radiation-induced conductivity are derived and compared with other methods. The result shows a good estimation of dark conductivity and radiation-induced conductivity in high-resistivity polymers, which enables a fast measurement of dielectric conductivity within about 600 rain after irradiation.
基金Supported by the Natural Science Foundation of Henan Provience(9902).
文摘This paper give some sufficient condition on the nonlinear cross section to insure thewell-posedness and asymptotic behavior of a class of time-dependent neutron transport equations inspaces of measures.
文摘In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.
基金Supported by the Special Science Foundation of the Education Committee of Shaanxi Province(03jk066)
文摘It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).
基金Supported by the Scientific Startup Foundation for Doctors of Northwest Normal University(Grant No.0002020203)the Innovation Fund Project for Higher Education of Gansu Province(Grant No.2020A-010)。
文摘The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_(γ)]is compact from Morrey space M_(q)^(p)(μ)into Morrey space M_(t)^(s)(μ)if and only if b∈Lip_(β)(μ).
基金the support from the National Natural Science Foundation of China(No.51905034,52275083)。
文摘There exists an increasing need for Milli-Arc-Seconds(MAS)accuracy pointing measurement for current and future space systems.To meet the 0.1″space pointing measurement accuracy requirements of spacecraft in future,the influence of spacecraft micro-vibration on a 0.1″Space Pointing Measuring Instrument(SPMI)is studied.A Quasi-Zero Stiffness Device(QZSD)with adaptive adjustment and variable stroke was proposed.Then,a series of micro-vibration experiments of the SPMI were carried out.The influence of the micro-vibration generated by Guidance Navigation Control(GNC)attitude control components under different attitudes on the SPMI was analyzed.Point spread function of image motion in micro-vibration was also derived.Further,the changes of image motion under the micro-vibration environment were evaluated by extracting the gray centroid of the images,and the experiment processes and results are deeply discussed.The results show that the firstorder frequency of the QZSD system is 0.114 Hz,and it is induced by a double pendulum system;the image motion of single flywheel spinning reached 0.015 pixels;whilst the image motion reached 0.03 pixels when three flywheels are combined spinning.These latest findings provide a beneficial theoretical and technical support for the development of spacecraft with 0·1″pointing accuracy.
