带变量核的分数次积分算子与局部Campanato函数生成的交换子在广义局部Morrey空间的有界性（英文）

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英文篇名：Boundedness of Commutators Generated by Fractional Integral Operators With Variable Kernel and Local Campanato Functions on Generalized Local Morrey Spaces 作者：默会霞 ; 薛红旸 英文作者：MO Huixia;XUE Hongyang;School of Sciences, Beijing University of Posts and Telecommunications; 关键词：分数次积分 ; 变量核 ; 交换子 ; 局部Campanato函数 ; 广义局部Morrey空间 英文关键词：fractional integral;;variable kernel;;commutator;;local Campanato function;;generalized local Morrey space 中文刊名：SXJZ 英文刊名：Advances in Mathematics 机构：北京邮电大学理学院; 出版日期：2017-09-15 出版单位：数学进展 年：2017 期：v.46 基金：supported by NSFC(No.11601035,No.11471050) 语种：英文; 页：SXJZ201705011 页数：10 CN：05 ISSN：11-2312/O1 分类号：117-126

摘要

设T_(Ω,a)是带变量核的分数次积分算子.本文证明了T_(Ω,α)在广义局部Morrey空间LM_(p,φ)~{x_0}的有界性,进一步还考虑了由T_(Ω,α)与局部Campanato函数生成的多线性交换子在广义局部Morrey空间的有界性.
        Suppose that T_(Ω,α) is the fractional integral operator with variable kernel. We prove the boundedness for T_(Ω,α) on the generalized local Morrey spaces LM_(p,φ)~{x_0}. The multilinear commutators generated by T_(Ω,α) and local Campanato functions are also considered.

引文

[1]Balakishiyev,A.S.,Guliyev,V.S.,Gurbuz,F.and Serbetci,A.,Sublinear operators with rough kernel generated by Calderón-Zygmund operators and their commutators on generalized local Morrey spaces,J.Inequal.Appl.,2015,2015:61,18 pages.
    [2]Chen,Y.P.,Ding,Y.and Li,R.,The boundedness for commutator of fractional integral operator with rough variable kernel,Potential Anal.,2013,38(1):119-142.
    [3]Ding,Y.,Weak type bounds for a class of rough operators with power weights,Proc.Amer.Math.Soc.,1997,125(10):2939-2942.
    [4]Ding,Y.,Chen,J.C.and Fan,D.S.,A class of integral operators with variable kernels on Hardy spaces,Chinese Ann.Math.Ser.A,2002,23(3):289-296(in Chinese).
    [5]Guliyev,V.S.,Local generalized Morrey spaces and singular integrals with rough kernel,Azerb.J.Math.,2013,3(2):79-94.
    [6]Guliyev,V.S.,Generalized local Morrey spaces and fractional integral operators with rough kernel,J.Math.Sci.(N.Y.),2013,193(2):211-227.
    [7]Mo,H.X.and Xue,H.Y.,Commutators generated by singular integral operators with variable kernels and local Campanato functions on generalized local Morrey spaces,Commun.Math.Anal.,2016,19(2):32-42.
    [8]Morrey,C.B.Jr.,On the solutions of quasi-linear elliptic partial differential equations,Trans.Amer.Math.Soc.,1938,43(1):126-166.
    [9]Muckenhoupt,B.and Wheeden,R.L.,Weighted norm inequalities for singular and fractional integrals,Trans.Amer.Math.Soc.,1971,161:249-258.
    [10]Shao,X.K.and Wang,S.P.,Boundedness of fractional operators with variable kernels on weighted Morrey spaces,J.Anhui Univ.Nat.Sci.,2015,39(1):21-24(in Chinese).
    [11]Zhang,P.and Chen,J.C.,A class of integral operators with variable kernels on the Herz-type Hardy spaces,Chinese Ann.Math.Ser.A,2004,25(5):561-570(in Chinese).
    [12]Zhang,P.and Zhao,K.,Commutators of integral operators with variable kernels on Hardy spaces,Proc.Indian Acad.Sci.Math.Sci.,2005,115(4):399-410.