LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional...LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey...In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).展开更多
For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case ...For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.展开更多
In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator esti...In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.展开更多
In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,...In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.展开更多
This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author...This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.展开更多
In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Mo...In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedn...Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.展开更多
. Let H2 = （-△）2 ＋ V2 be the Schr6dinger type operator, where V satisfies reverse HSlder inequality. In this paper, we establish the Lp boundedness for V2 H2- 1, H21 V2, VH2- 1/2 and Hfl/2V, and that of their comm.... Let H2 = （-△）2 ＋ V2 be the Schr6dinger type operator, where V satisfies reverse HSlder inequality. In this paper, we establish the Lp boundedness for V2 H2- 1, H21 V2, VH2- 1/2 and Hfl/2V, and that of their commutators. We also prove that H^IV2, Hfl/2V are bounded from BMOL to BMOL.展开更多
In this paper, we give some creative characterizations of Campanato spaces via the boundedness of commutators associated with the Calderon-Zygmund singular integral operator, fractional integrals and Hardy type operat...In this paper, we give some creative characterizations of Campanato spaces via the boundedness of commutators associated with the Calderon-Zygmund singular integral operator, fractional integrals and Hardy type operators. Furthermore, we put forward a few problems on the characterizations of Campanato type spaces via the boundedness of commutators.展开更多
To enhance power flow regulation in scenarios involving large-scale renewable energy transmission via high-voltage direct current(HVDC)links and multi-infeed DC systems in load-center regions,this paper proposes a hyb...To enhance power flow regulation in scenarios involving large-scale renewable energy transmission via high-voltage direct current(HVDC)links and multi-infeed DC systems in load-center regions,this paper proposes a hybrid modular multilevel converter–capacitor-commutated line-commutated converter(MMC-CLCC)HVDC transmission system and its corresponding control strategy.First,the system topology is constructed,and a submodule configuration method for the MMC—combining full-bridge submodules(FBSMs)and half-bridge submodules(HBSMs)—is proposed to enable direct power flow reversal.Second,a hierarchical control strategy is introduced,includingMMCvoltage control,CLCC current control,and a coordinationmechanism,along with the derivation of the hybrid system’s power flow reversal characteristics.Third,leveraging the CLCC’s fast current regulation and theMMC’s negative voltage control capability,a coordinated power flow reversal control strategy is developed.Finally,an 800 kV MMC-CLCC hybrid HVDC system is modeled in PSCAD/EMTDC to validate the power flow reversal performance under a high proportion of full-bridge submodule configuration.Results demonstrate that the proposed control strategy enables rapid(1-s transition)and smooth switching of bidirectional power flow without modifying the structure of primary equipment:the transient fluctuation ofDC voltage from the rated value(UdcN)to themaximumreverse voltage(-kUdcN)is less than 5%;the DC current strictly follows the preset characteristic curve with a deviation of≤3%;the active power reverses continuously,and the system maintains stable operation throughout the reversal process.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ...It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).展开更多
Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded...Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.展开更多
Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multil...Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO（μ） functions.展开更多
Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2...Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.展开更多
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
文摘LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
文摘In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).
基金partially supported by the research grant of Macao University of Science and Technology(FRG-22-075-MCMS)the Macao Government Research Funding(FDCT0128/2022/A)+2 种基金the Science and Technology Development Fund of Macao SAR(005/2022/ALC)the Science and Technology Development Fund of Macao SAR(0045/2021/A)Macao University of Science and Technology(FRG-20-021-MISE)。
文摘For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.
文摘In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.
基金Supported by the National Natural Science Foundation of China(11671397,11571160,12071052)the Yue Qi Young Scholar of China University of Mining and Technology(Beijing)。
文摘In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.
基金Supported by the Key Project of the Education Department of Fujian Province(JZ230054)the Sanming University's High-Level Talent Introduction Project(23YG09)the Natural Science Foundation of Fujian Province(2024J01903)。
文摘This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.
基金Supported by the National Natural Science Foundation of China(Grant No.12201500)。
文摘In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.
文摘Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.
基金Supported by the National Natural Science Foundation of China(11261023,11401269,11461033)the Natural Science Foundation of Jiangxi Province(20142BAB201003)
文摘. Let H2 = （-△）2 ＋ V2 be the Schr6dinger type operator, where V satisfies reverse HSlder inequality. In this paper, we establish the Lp boundedness for V2 H2- 1, H21 V2, VH2- 1/2 and Hfl/2V, and that of their commutators. We also prove that H^IV2, Hfl/2V are bounded from BMOL to BMOL.
基金partially supported by the Fundamental Research Funds for the Central Universities (Grant No. 2012CXQT09)the Key Laboratory of Mathematics and Complex System of Beijing Normal University and the NSF of China (Grant Nos. 11271175, 11561057, 11301249, 11471309)
文摘In this paper, we give some creative characterizations of Campanato spaces via the boundedness of commutators associated with the Calderon-Zygmund singular integral operator, fractional integrals and Hardy type operators. Furthermore, we put forward a few problems on the characterizations of Campanato type spaces via the boundedness of commutators.
基金supported by Science and Technology Project of the headquarters of the State Grid Corporation of China(No.5500-202324492A-3-2-ZN).
文摘To enhance power flow regulation in scenarios involving large-scale renewable energy transmission via high-voltage direct current(HVDC)links and multi-infeed DC systems in load-center regions,this paper proposes a hybrid modular multilevel converter–capacitor-commutated line-commutated converter(MMC-CLCC)HVDC transmission system and its corresponding control strategy.First,the system topology is constructed,and a submodule configuration method for the MMC—combining full-bridge submodules(FBSMs)and half-bridge submodules(HBSMs)—is proposed to enable direct power flow reversal.Second,a hierarchical control strategy is introduced,includingMMCvoltage control,CLCC current control,and a coordinationmechanism,along with the derivation of the hybrid system’s power flow reversal characteristics.Third,leveraging the CLCC’s fast current regulation and theMMC’s negative voltage control capability,a coordinated power flow reversal control strategy is developed.Finally,an 800 kV MMC-CLCC hybrid HVDC system is modeled in PSCAD/EMTDC to validate the power flow reversal performance under a high proportion of full-bridge submodule configuration.Results demonstrate that the proposed control strategy enables rapid(1-s transition)and smooth switching of bidirectional power flow without modifying the structure of primary equipment:the transient fluctuation ofDC voltage from the rated value(UdcN)to themaximumreverse voltage(-kUdcN)is less than 5%;the DC current strictly follows the preset characteristic curve with a deviation of≤3%;the active power reverses continuously,and the system maintains stable operation throughout the reversal process.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
文摘It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).
文摘Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.
基金supported by National Natural Science Foundation of China (10701078)supported by National Science Foundation for Distinguished Young Scholars (10425106)
文摘Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO（μ） functions.
基金Supported by National 973 Project(G.19990751)the SEDF of China(20040027001)
文摘Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
