Weighted inequalities for multilinear fractional integral operators

被引：128
作者：
Moen, Kabe [1 ]
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
来源：
COLLECTANEA MATHEMATICA | 2009年 / 60卷 / 02期
基金：
美国国家科学基金会;
关键词：
Fractional integrals; maximal operators; weighted norm inequalities; multilinear operators; NORM INEQUALITIES; SINGULAR-INTEGRALS; MAXIMAL OPERATORS;
D O I：
10.1007/BF03191210
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A weighted theory for multilinear fractional integral operators and maximal functions is presented. Sufficient conditions for the two weight inequalities of these operators are found, including "power and logarithmic bumps" and an A(infinity) condition. For one weight inequalities a necessary and sufficient condition is then obtained as a consequence of the two weight inequalities. As an application, Poincare and Sobolev inequalities adapted to the multilinear setting are presented.
引用
收藏
页码：213 / 238
页数：26
相关论文
共 50 条
  • [1] Weighted inequalities for multilinear fractional integral operators
    Kabe Moen
    Collectanea mathematica, 2009, 60 : 213 - 238
  • [2] Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators
    Pradolini, Gladis
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 367 (02) : 640 - 656
  • [3] Multiple weighted estimates for commutators of multilinear fractional integral operators
    Chen SongQing
    Wu HuoXiong
    SCIENCE CHINA-MATHEMATICS, 2013, 56 (09) : 1879 - 1894
  • [4] Weighted endpoint estimates for commutators of multilinear fractional integral operators
    Yan, Xuefang
    Xue, Limei
    Li, Wenming
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2012, 62 (02) : 347 - 359
  • [5] Multiple weighted estimates for commutators of multilinear fractional integral operators
    CHEN SongQing
    WU HuoXiong
    ScienceChina(Mathematics), 2013, 56 (09) : 1879 - 1894
  • [6] Multiple weighted estimates for commutators of multilinear fractional integral operators
    SongQing Chen
    HuoXiong Wu
    Science China Mathematics, 2013, 56 : 1879 - 1894
  • [7] Sharp weighted bounds for fractional integral operators
    Lacey, Michael T.
    Moen, Kabe
    Perez, Carlos
    Torres, Rodolfo H.
    JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (05) : 1073 - 1097
  • [8] Weighted inequalities for multilinear fractional operators in Dunkl setting
    Mukherjee, Suman
    Parui, Sanjay
    JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2022, 13 (03)
  • [9] Weighted endpoint estimates for commutators of multilinear fractional integral operators
    Xuefang Yan
    Limei Xue
    Wenming Li
    Czechoslovak Mathematical Journal, 2012, 62 : 347 - 359
  • [10] Sharp weighted inequalities for multilinear fractional maximal operators and fractional integrals
    Li, Kangwei
    Moen, Kabe
    Sun, Wenchang
    MATHEMATISCHE NACHRICHTEN, 2015, 288 (5-6) : 619 - 632
12345