HARDY-LITTLEWOOD, BESSEL-RIESZ, AND FRACTIONAL INTEGRAL OPERATORS IN ANISOTROPIC MORREY AND CAMPANATO SPACES

被引：12

作者：

Ruzhansky, Michael ^{[1
]}

Suragan, Durvudkhan ^{[2
]}

Yessirkegenov, Nurgissa ^{[1
,3
]}

机构：

[1] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England

[2] Nazarbayev Univ, Sch Sci & Technol, Dept Math, 53 Kabanbay Batyr Ave, Astana 010000, Kazakhstan

[3] Inst Math & Math Modelling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2018年 / 21卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

fractional integral operator; generalized local (central) Morrey space; Campanato space; Hardy-Littlewood maximal operator; Bessel-Riesz operator; Olsen type inequality; homogeneous Lie group; CAFFARELLI-KOHN-NIRENBERG; MAXIMAL OPERATOR; RELLICH INEQUALITIES; BOUNDEDNESS; POTENTIALS;

D O I：

10.1515/fca-2018-0032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze local (central) Morrey spaces, generalized local (central) Morrey spaces and Campanato spaces on homogeneous groups. The boundedness of the Hardy-Littlewood maximal operator, Bessel-Riesz operators, generalized Bessel-Riesz operators and generalized fractional integral operators in generalized local (central) Morrey spaces on homogeneous groups is shown. Moreover, we prove the boundedness of the modified version of the generalized fractional integral operator and Olsen type inequalities in Campanato spaces and generalized local (central) Morrey spaces on homogeneous groups, respectively. Our results extend results known in the isotropic Euclidean settings, however, some of them are new already in the standard Euclidean cases.

引用

页码：577 / 612

页数：36

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