On the boundedness of the multilinear fractional integral operators

被引：12
|
作者：
Kokilashvili, Vakhtang [1 ,2 ]
Mastylo, Mieczyslaw [3 ,4 ]
Meskhi, Alexander [1 ,5 ]
机构：
[1] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, Dept Math Anal, GE-0177 Tbilisi, Georgia
[2] Int Black Sea Univ, GE-0131 Tbilisi, Georgia
[3] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland
[4] Polish Acad Sci, Poznan Branch, Inst Math, PL-61614 Poznan, Poland
[5] Georgian Tech Univ, Fac Informat & Control Syst, Dept Math, Tbilisi, Georgia
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 94卷
基金：
美国国家科学基金会;
关键词：
Multilinear fractional integrals; Boundedness; Weighted inequality; WEIGHTED INEQUALITIES;
D O I：
10.1016/j.na.2013.08.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We derive necessary and sufficient conditions for a weight v governing the weighted inequality (integral(Rn)vertical bar I-alpha((f) over right arrow)(x)vertical bar(q) v(x)dx)(1/q) <= c Pi(m)(i=1)(integral(Rn)vertical bar f(i)(x)vertical bar(pi)dx)(1/pi), where I-alpha is the multilinear fractional integral operator. The derived condition is of D. Adams type and any additional assumption on the weight v is not assumed. (C) 2013 Elsevier Ltd. All rights reserved.
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页码：142 / 147
页数：6
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