与微分算子相关的分数次积分交换子的有界性
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摘要
利用分数次积分算子交换子,在Lebesgue空间及Morrey-Herz空间上的有界性,研究了在Lebesgue空间,与微分算子相关的分数次积分算子交换子的有界性。证明在MorreyHerz空间上,与微分算子相关的分数次积分算子交换子的有界性。
Using the boundedness result of commutators of fractional integral,on Lebesgue spaces and Morrey-Herz spaces.The boundedness of commutators of fractional integral operators associated with differential operator on Lebesgue spaces is obtained.Based on this,it is proved that the commutators of fractional integral operators associated with differential operator is bounded on Morrey-Herz spaces.
Using the boundedness result of commutators of fractional integral,on Lebesgue spaces and Morrey-Herz spaces.The boundedness of commutators of fractional integral operators associated with differential operator on Lebesgue spaces is obtained.Based on this,it is proved that the commutators of fractional integral operators associated with differential operator is bounded on Morrey-Herz spaces.
引文
[1]Chander S.A note on commutators[J].Indiana University Mathematics Journal,1982,31(1):7-16.
[2]Paluszyński M.Characterization of Bosev spaces via the commutator operator of Coifman,Rochberg and Weiss[J].Indiana University Mathematics Journal,1991,44(1):1-17.
[3]Martell J M.Sharp maximal function associated with approximations of the identity in spaces of homogeneous type and applications[J].Studia Mathematica,2004,161(2):113-145.
[4]Xuan Thinh Duong.On commutators of fractional integrals[J].Proceedings of the American Mathematical Society,2004,132(12):3549-3557.
[5]陈冬香,张锐.奇异积分算子在Triebel-Lizorkin空间的有界性[J].北京师范大学报:自然科学版,2008,44(2):143-145.
[6]Wang H.Some estimates for commutators of fractional integrals associated to operators with Gaussian kernel bounds on weighted Morrey spaces[J].Analysis in Theory and Applications,2013,29(1):72-85.
[7]张立平,赵凯,耿素丽.与微分算子相关的分数次积分算子交换子的有界性[J].云南大学学报:自然科学版,2004,36(1):12-15.
[8]Lu S,Yang D,Hu G.Herz type spaces and their application[M].Beijing:Science Press,2008.
[9]Lu S,Xu L.Boundedness of rough singular integral operator on the homogeneous Morrey-Herz spaces[J].Hokkaido Mathematical Journal,2005,34(34):299-314.
[10]Wu J.Boundedness for commutator of fractional integrals on Herz-Morrey spaces with variable exponent[J].Mathematics,2014,54(3):483-495.
[11]王洪斌,付尊伟,刘宗光.变指标Lebesgue空间上Marcinkeiwicz积分高阶交换子[J].数学物理学报,2012,32(6):1092-1101.
[12]陶双平,武江龙.齐次Morrey-Herz空间上粗糙核高阶交换子的有界性[J].数学进展,2007,36(5):607-616.
[13]王海莲,谢如龙.Littlewood-Paley算子高阶交换子在齐次Morrey-Herz空间上的有界性[J].安庆师范学院学报:自然科学版,2009,15(1):10-12.
[14]赵凯,王永刚,王磊.非双倍测度下Calderón-Zygmund算子交换子在Morrey-Herz空间上的有界性[J].应用数学,2012,25(1):40-46.
[15]Wu C.Boundedness of commutators of fractional integral operators on Herz space and Morrey-Herz space[J].Journal of Xuzhou Normal University,2010,28(1):20-24.
[16]Wu C,Shu L.Boundedness for the commutators of integral operators with rough kernels on Morrey-Herz spaces[J].Journal of Sichuan Normal University,2013,36(5):696-702.
[2]Paluszyński M.Characterization of Bosev spaces via the commutator operator of Coifman,Rochberg and Weiss[J].Indiana University Mathematics Journal,1991,44(1):1-17.
[3]Martell J M.Sharp maximal function associated with approximations of the identity in spaces of homogeneous type and applications[J].Studia Mathematica,2004,161(2):113-145.
[4]Xuan Thinh Duong.On commutators of fractional integrals[J].Proceedings of the American Mathematical Society,2004,132(12):3549-3557.
[5]陈冬香,张锐.奇异积分算子在Triebel-Lizorkin空间的有界性[J].北京师范大学报:自然科学版,2008,44(2):143-145.
[6]Wang H.Some estimates for commutators of fractional integrals associated to operators with Gaussian kernel bounds on weighted Morrey spaces[J].Analysis in Theory and Applications,2013,29(1):72-85.
[7]张立平,赵凯,耿素丽.与微分算子相关的分数次积分算子交换子的有界性[J].云南大学学报:自然科学版,2004,36(1):12-15.
[8]Lu S,Yang D,Hu G.Herz type spaces and their application[M].Beijing:Science Press,2008.
[9]Lu S,Xu L.Boundedness of rough singular integral operator on the homogeneous Morrey-Herz spaces[J].Hokkaido Mathematical Journal,2005,34(34):299-314.
[10]Wu J.Boundedness for commutator of fractional integrals on Herz-Morrey spaces with variable exponent[J].Mathematics,2014,54(3):483-495.
[11]王洪斌,付尊伟,刘宗光.变指标Lebesgue空间上Marcinkeiwicz积分高阶交换子[J].数学物理学报,2012,32(6):1092-1101.
[12]陶双平,武江龙.齐次Morrey-Herz空间上粗糙核高阶交换子的有界性[J].数学进展,2007,36(5):607-616.
[13]王海莲,谢如龙.Littlewood-Paley算子高阶交换子在齐次Morrey-Herz空间上的有界性[J].安庆师范学院学报:自然科学版,2009,15(1):10-12.
[14]赵凯,王永刚,王磊.非双倍测度下Calderón-Zygmund算子交换子在Morrey-Herz空间上的有界性[J].应用数学,2012,25(1):40-46.
[15]Wu C.Boundedness of commutators of fractional integral operators on Herz space and Morrey-Herz space[J].Journal of Xuzhou Normal University,2010,28(1):20-24.
[16]Wu C,Shu L.Boundedness for the commutators of integral operators with rough kernels on Morrey-Herz spaces[J].Journal of Sichuan Normal University,2013,36(5):696-702.