WEIGHTED ESTIMATES OF MULTILINEAR FRACTIONAL INTEGRAL OPERATORS FOR RADIAL FUNCTIONS

被引：1
作者：
Komori-Furuya, Yasuo [1 ]
Sato, Enji [2 ]
机构：
[1] Tokai Univ, Sch Sci, Dept Math, Hiratsuka, Kanagawa 2591299, Japan
[2] Yamagata Univ, Fac Sci, Dept Math Sci, Yamagata 9908560, Japan
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2020年 / 23卷 / 01期
关键词：
Multilinear fractional integral operator; radial function; power weight; CAFFARELLI-KOHN-NIRENBERG; INEQUALITIES;
D O I：
10.7153/mia-2020-23-19
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Moen (2009) proved weighted estimates for multilinear fractional integral operators. We consider weighted estimates of these operators for radial functions and power weights and obtain a better result. Our result is a multilinear valiant of the one by De Napoli, Drelichman and Duran (2011). As applications, we get improvements of the bilinear Caffarelli-Kohn-Nirenberg's inequality.
引用
收藏
页码：245 / 256
页数：12
相关论文
共 11 条
  • [1] [Anonymous], 1970, SINGULAR INTEGRALS D
  • [2] CAFFARELLI L, 1984, COMPOS MATH, V53, P259
  • [3] Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrability
    D'Ancona, Piero
    Luca, Renato
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (02) : 1061 - 1079
  • [4] ON WEIGHTED INEQUALITIES FOR FRACTIONAL INTEGRALS OF RADIAL FUNCTIONS
    De Napoli, Pablo L.
    Drelichman, Irene
    Duran, Ricardo G.
    [J]. ILLINOIS JOURNAL OF MATHEMATICS, 2011, 55 (02) : 575 - 587
  • [5] IMPROVED CAFFARELLI-KOHN-NIRENBERG AND TRACE INEQUALITIES FOR RADIAL FUNCTIONS
    De Napoli, Pablo L.
    Drelichman, Irene
    Duran, Ricardo G.
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2012, 11 (05) : 1629 - 1642
  • [6] Fractional integrals on radial functions with applications to weighted inequalities
    Duoandikoetxea, Javier
    [J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2013, 192 (04) : 553 - 568
  • [7] Grafakos L, 2009, GRAD TEXTS MATH, V250, P1, DOI [10.1007/978-0-387-09434-2_6, 10.1007/978-0-387-09432-8_1]
  • [8] New maximal functions and multiple weights for the multilinear Calderon-Zygmund theory
    Lerner, Andrei K.
    Ombrosi, Sheldy
    Perez, Carlos
    Torres, Rodolfo H.
    Trujillo-Gonzalez, Rodrigo
    [J]. ADVANCES IN MATHEMATICS, 2009, 220 (04) : 1222 - 1264
  • [9] Sharp one-weight and two-weight bounds for maximal operators
    Moen, Kabe
    [J]. STUDIA MATHEMATICA, 2009, 194 (02) : 163 - 180
  • [10] Weighted inequalities for multilinear fractional integral operators
    Moen, Kabe
    [J]. COLLECTANEA MATHEMATICA, 2009, 60 (02) : 213 - 238
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