非散度型椭圆方程的解在加权Morrey-Herz空间上的正则性

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英文篇名：Regularity in weighted Morrey-Herz spaces of solutions to nondivergence elliptic equations 作者：陶双平 ; 马骊 英文作者：TAO Shuang-ping;MA Li;College of Mathematics and Statistics,Northwest Normal University; 关键词：奇异积分 ; VMO空间 ; 加权Morrey-Herz空间 ; 椭圆方程 英文关键词：singular integral;;VMO space;;weighted Morrey-Herz space;;elliptic equation 中文刊名：XBSF 英文刊名：Journal of Northwest Normal University(Natural Science) 机构：西北师范大学数学与统计学院; 出版日期：2013-09-15 出版单位：西北师范大学学报(自然科学版) 年：2013 期：v.49;No.172 基金：国家自然科学基金资助项目(11161042,11071250) 语种：中文; 页：XBSF201305003 页数：7 CN：05 ISSN：62-1087/N 分类号：12-18

摘要

利用Lebesgue空间上的有界性结果,建立了奇异积分算子及其交换子在加权Morrey-Herz空间上的有界性,并由此得到了VMO系数非散度型二阶椭圆方程Dirichlet问题的强解在加权Morrey-Herz空间上的整体正则性.
        By applicating the boundedness results in Lebesgue spaces,the boundedness of singular integral operators and its commutators is established in the weighted Morrey-Herz spaces.Then,the global regularity of strong solutions is obtained to the Dirichlet problem on the second-order elliptic equations with VMO coefficients in nondivergence form in the weighted Morrey-Herz spaces.

引文

[1]LU Shan-zhen,YABUTA K,YANG Da-chun.Boundedness of some sublinear operators in weighted Herz-type spaces[J].Kodai Math J,2000,23:391-410.
    [2]LU Shan-zhen.Herz type spaces[J].Adv in Math(Chinese),2004,33:257-272.
    [3]LU Shan-zhen,YANG Da-chun,HU Guo-en.Herz Type Spaces and Their Applications[M].Mathematics Monograph Series 10,Beijing:Science Press,2008.
    [4]KOMORI Y,MATSUOKA K.Boundedness of several operators on weighted Herz spaces[J].J Funct Spaces Appl,2009,7:1-12.
    [5]FAN Da-shan,LU Shan-zhen,YANG Da-chun.Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients[J].Georgian Math J,1998,5:425-440.
    [6]LU Shan-zhen,TAO Shuang-ping.Global regularity in homogeneous Morrey-Herz space of solutions to nondivergence elliptic equations with VMO coefficients[J].J Partial Diff Eqs,2007,20(2):97-113.
    [7]RAGUSA M A.Homogeneous Herz spaces and regularity results[J].Nonlinear Analysis,Series A:Theory,Methods and Applications,2009,71(12):1909-1914.
    [8]RAGUSA M A.Parabolic Herz spaces and their applications[J].Appl Math Lett,2012,25(10):1270-1273.
    [9]GUO Yu-xing,JIANG Yin-sheng.Weighted Herz spaces and regularity results[J].J Funct Spaces Appl,2012,Article ID 283730,13pages.
    [10]CHIARENZA F,FRASCA M,LONGO P.Interior W2,p estimates for nondivergence elliptic equations with discontinuous coefficients[J].Ricerche Mat,1991,40:149-168.
    [11]CHIARENZA F,FRASCA M,LONGO P.W2,p-solvability of Dirichlet problem for nondivergence elliptic equations with VMO coefficients[J].Trans Amer Math Soc,1993,336:841-853.
    [12]瞿萌,康金强.Calderon-Zygmund算子多线性交换子在加权Morrey-Herz空间上的有界性[J].数学研究,2011,44(1):69-75.
    [13]LU Shan-zhen,DING Yong,YAN Dun-yan.Singular Integrals and Related Topics[M].Singapore:World Scientific Publishing Co.Pte.Ltd,2007.