In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewi...In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q （f） from ｜｜f｜｜Fp^oq（Rn） into Lp （Rn）.展开更多
In this paper,the authors prove that the commutator[b,T]of the parabolic singular integrals is a compact operator on Lp(Rn)(1【p【∞)if and only if b∈VMO(Rn,ρ).The result is substantial improvement and extension of ...In this paper,the authors prove that the commutator[b,T]of the parabolic singular integrals is a compact operator on Lp(Rn)(1【p【∞)if and only if b∈VMO(Rn,ρ).The result is substantial improvement and extension of some known results.展开更多
Let [b, T] be the commutator of parabolic singular integral T. In this paper, the authors prove that the boundedness of [b, T] on the generalized Morrey spaces implies b ∈ BMO（Rn, ρ）. The results in this paper imp...Let [b, T] be the commutator of parabolic singular integral T. In this paper, the authors prove that the boundedness of [b, T] on the generalized Morrey spaces implies b ∈ BMO（Rn, ρ）. The results in this paper improve and extend the Komori and Mizuhara＇s results.展开更多
We prove weighted mixed-norm Lqt(W2,px)and Lqt(C2,αx)estimates for 1<p,q<∞and 0<α<1,weighted mixed weak-type estimates for q=1,L∞t(Lpx)−BMOt(W2,px)and L∞t(Cαx)−BMOt(C2,xx),and a.e.pointwise formulas ...We prove weighted mixed-norm Lqt(W2,px)and Lqt(C2,αx)estimates for 1<p,q<∞and 0<α<1,weighted mixed weak-type estimates for q=1,L∞t(Lpx)−BMOt(W2,px)and L∞t(Cαx)−BMOt(C2,xx),and a.e.pointwise formulas for derivatives,for the solutions u=u(t,x)to parabolic equations of the form∂tu−aij(t)∂iju+u=f,t∈,x∈n and for the Cauchy problem{∂tv−aij(t)∂ijv+v=fv(0,x)forfort>0,x∈Rn.x∈Rn,The coefficients a(t)=(aij(t))are just bounded,measurable,symmetric and uniformly elliptic.Furthermore,we show strong,weak type and BMO-Sobolev estimates with parabolic Muckenhoupt weights.It is quite remarkable that most of our results are new even for the classical heat equation∂tu−Δu+u=f.展开更多
基金Supported in part by National Natural Foundation of China (Grant No. 11071250)
文摘In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q （f） from ｜｜f｜｜Fp^oq（Rn） into Lp （Rn）.
基金supported by National Natural Science Foundation of China(Grant Nos.10931001,10901017)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20090003110018)Natural Science Foundation of Zhejiang Province(Grant No.Y7080325)
文摘In this paper,the authors prove that the commutator[b,T]of the parabolic singular integrals is a compact operator on Lp(Rn)(1【p【∞)if and only if b∈VMO(Rn,ρ).The result is substantial improvement and extension of some known results.
基金supported by the National Natural Science Foundation of China(No.10901017)Program for New Century Excellent Talents in University of China(Grant:NCET-11-0574)+3 种基金the Fundamental Research Funds for the Central Universities(FRF-TP-12-006B)supported by the National Natural Science Foundation of China(No.11371057)Research Fund for the Doctoral Program of Higher Education(Grant:20130003110003)Program for Changjiang Scholars and Innovative Research Team in University
文摘Let [b, T] be the commutator of parabolic singular integral T. In this paper, the authors prove that the boundedness of [b, T] on the generalized Morrey spaces implies b ∈ BMO（Rn, ρ）. The results in this paper improve and extend the Komori and Mizuhara＇s results.
基金Supported by National Natural Science Foundation of China （Grant No. 11071250） NWNU-KJCXGC-3-47 The authors would like to express their deep thanks to the referee for his/her very careful reading and many valuable comments and suggestions
文摘In this paper, the authors give the boundedness on Triebel-Lizorkin spaces for the parabolic singular integral with rough kernel and its commutator.
基金supported by Simons Foundation(Grant No.580911(Stinga))Ministerio de Economía y Competitividad/Fondo Europeo de Desarrollo Regional from Government of Spain(Grant No.MTM2015-66157-C2-1-P(Torrea))。
文摘We prove weighted mixed-norm Lqt(W2,px)and Lqt(C2,αx)estimates for 1<p,q<∞and 0<α<1,weighted mixed weak-type estimates for q=1,L∞t(Lpx)−BMOt(W2,px)and L∞t(Cαx)−BMOt(C2,xx),and a.e.pointwise formulas for derivatives,for the solutions u=u(t,x)to parabolic equations of the form∂tu−aij(t)∂iju+u=f,t∈,x∈n and for the Cauchy problem{∂tv−aij(t)∂ijv+v=fv(0,x)forfort>0,x∈Rn.x∈Rn,The coefficients a(t)=(aij(t))are just bounded,measurable,symmetric and uniformly elliptic.Furthermore,we show strong,weak type and BMO-Sobolev estimates with parabolic Muckenhoupt weights.It is quite remarkable that most of our results are new even for the classical heat equation∂tu−Δu+u=f.
