Two-Weight Norm Estimates for Multilinear Fractional Integrals in Classical Lebesgue Spaces

被引：0
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作者：
Vakhtang Kokilashvili
Mieczysław Mastyło
Alexander Meskhi
机构：
[1] A. Razmadze Mathematical Institute I. Javakhishvili Tbilisi State University 6,
[2] I. Javakhishvili Tbilisi State University,undefined
[3] Faculty of Mathematics and Computer Science Adam Mickiewicz University Poznań and Institute of Mathematics Polish Academy of Sciences (Poznań branch) Umultowska,undefined
[4] A. Razmadze Mathematical Institute I. Javakhishvili Tbilisi State University 6,undefined
[5] Department of Mathematics,undefined
[6] Faculty of Informatics and Control Systems Georgian Technical University 77,undefined
来源：
Fractional Calculus and Applied Analysis | 2015年 / 18卷
关键词：
Primary 42B25; Secondary 42B35; multilinear fractional integrals; multi(sub)linear strong fractional maximal operators; boundedness; two-weight inequality; trace inequality; Fefferman-Stein inequality;
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摘要：
We derive criteria governing two-weight estimates for multilinear fractional integrals and appropriate maximal functions. The two and one weight problems for multi(sub)linear strong fractional maximal operators are also studied; in particular, we derive necessary and sufficient conditions guaranteeing the trace type inequality for this operator. We also establish the Fefferman-Stein type inequality, and obtain one-weight criteria when a weight function is of product type. As a consequence, appropriate results for multilinear Riesz potential operator with product kernels follow.
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页码：1146 / 1163
页数：17
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