The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (?Δ)?α/2 are extended to the generalised fractional integrals L –α/2 for 0 < α < n, where L=?div A? is a uniformly complex elliptic opera...The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (?Δ)?α/2 are extended to the generalised fractional integrals L –α/2 for 0 < α < n, where L=?div A? is a uniformly complex elliptic operator with bounded measurable coefficients in ?n.展开更多
The authors prove the Hardy-Littlewood-Sobolev theorems for generalized fractional integrals L?α/2 for 0 < α < n/m, where L is a complex elliptic operator of arbitrary order 2m on Rn.
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
We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argum...We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.展开更多
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
This paper establishes some strong type and weak type estimates for commutator [b,I1] on Herz-type spaces, where b E BMO(Rn) and I1 is a fractional integration with O < l < n.
This paper introduces the class of seasonal fractionally integrated autoregressive<span style="font-family:Verdana;"> moving average</span><span style="font-family:Verdana;">-<...This paper introduces the class of seasonal fractionally integrated autoregressive<span style="font-family:Verdana;"> moving average</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">generalized conditional heteroskedastisticty (SARFIMA-</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">GARCH) models, with level shift type intervention that are capable of capturing simultaneously four key features of time series: seasonality, long range dependence, volatility and level shift. The main focus is on modeling seasonal level shift (SLS) in fractionally integrated and volatile processes. A natural extension of the seasonal level shift detection test of the mean for a realization of time series satisfying SLS-SARFIMA and SLS-GARCH models w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> derived. Test statistics that are useful to examine if seasonal level shift in a</span><span style="font-family:Verdana;">n</span><span style="font-family:Verdana;"> SARFIMA-GARCH model </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> statistically plausible were established. Estimation of SLS-SARFIMA and SLS-GARCH parameters w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> also considered.</span>展开更多
BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their s...BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA.展开更多
In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for cl...In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.展开更多
In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the bo...In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.展开更多
In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) i...The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.展开更多
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable coup...Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.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 ∠= -△Hn＋ V be the Schrdinger operator on the Heisenberg groups Hn,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates o...Let ∠= -△Hn＋ V be the Schrdinger operator on the Heisenberg groups Hn,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠.展开更多
In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional ...In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.展开更多
In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β...In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).展开更多
In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagran...In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.展开更多
In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish th...In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.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
基金This work was supported by the National Natural Science Foundation of China(Grant No.1017111) Foundation of Advanced Research Center,Zhongshan University.
文摘The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (?Δ)?α/2 are extended to the generalised fractional integrals L –α/2 for 0 < α < n, where L=?div A? is a uniformly complex elliptic operator with bounded measurable coefficients in ?n.
基金Project supported by the National Natural Science Foundation of China (No.10171111, No.10371734)and the Foundation of Advanced Research Center, Zhongshan University.
文摘The authors prove the Hardy-Littlewood-Sobolev theorems for generalized fractional integrals L?α/2 for 0 < α < n/m, where L is a complex elliptic operator of arbitrary order 2m on Rn.
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 National Natural Science Foundation of China(Grant No.62363005).
文摘We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.
文摘In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
文摘This paper establishes some strong type and weak type estimates for commutator [b,I1] on Herz-type spaces, where b E BMO(Rn) and I1 is a fractional integration with O < l < n.
文摘This paper introduces the class of seasonal fractionally integrated autoregressive<span style="font-family:Verdana;"> moving average</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">generalized conditional heteroskedastisticty (SARFIMA-</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">GARCH) models, with level shift type intervention that are capable of capturing simultaneously four key features of time series: seasonality, long range dependence, volatility and level shift. The main focus is on modeling seasonal level shift (SLS) in fractionally integrated and volatile processes. A natural extension of the seasonal level shift detection test of the mean for a realization of time series satisfying SLS-SARFIMA and SLS-GARCH models w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> derived. Test statistics that are useful to examine if seasonal level shift in a</span><span style="font-family:Verdana;">n</span><span style="font-family:Verdana;"> SARFIMA-GARCH model </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> statistically plausible were established. Estimation of SLS-SARFIMA and SLS-GARCH parameters w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> also considered.</span>
基金Supported by the Key Scientific Research Project of Universities in Henan Province,No.21A330004Natural Science Foundation in Henan Province,No.222300420265.
文摘BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA.
基金Supported by the National Natural Sciences Foundation of China (10771110)the Natural Science Founda- tion of Ningbo City (2006A610090)
文摘In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.
基金Supported by the National Natural Science Foundation of China(11271330,11226104,11226108)the Jiangxi Natural Science Foundation of China(20114BAB211007)the Science Foundation of Jiangxi Education Department(GJJ13703)
文摘In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.
基金Supported by the National Natural Science Foundation of China(11271330)
文摘In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
基金Supported by the973Project( G1 9990 75 1 0 5 ) and the National Natural Science Foundation of China( 1 0 2 71 0 1 6)
文摘The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.
基金supported by the National Natural Science Foundation of China(1127100861072147+1 种基金11071159)the First-Class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project(A13-0101-12-004)
文摘Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.
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.
文摘Let ∠= -△Hn＋ V be the Schrdinger operator on the Heisenberg groups Hn,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠.
文摘In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.
基金Supported by the National Natural Science Foundation of China(Grant No.11661075).
文摘In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).
基金Project supported by the National Natural Science Foundations of China(Grant Nos.11272287 and 11472247)the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT)(Grant No.IRT13097)
文摘In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.
基金Supported by the Anhui Polytechnic University Foundation for Recruiting Talent(2011YQQ004)Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2011A032)+1 种基金Supported by the Young Teachers Program of Anhui Province(2006jql042)Supported by the Grant for Younth of Anhui Polytechnic University (2010YQ047)
文摘In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.
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).
