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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Volume 27, Issue 5

Issues

Weighted multilinear Hardy operators and commutators

Zun Wei Fu / Shu Li Gong / Shan Zhen Lu
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China
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/ Wen Yuan
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China
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Published Online: 2014-01-21 | DOI: https://doi.org/10.1515/forum-2013-0064

Abstract

In this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight functions so that the commutators of the weighted multilinear Hardy operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Riemann–Liouville and Weyl.

Keywords: Weighted Hardy operator; multilinear operator; BMO; Morrey space; commutator

MSC: 47G10; 47H60; 47A63; 47A30

About the article

Received: 2013-04-24

Revised: 2013-09-30

Published Online: 2014-01-21

Published in Print: 2015-09-01


Funding Source: NSF of China

Award identifier / Grant number: 11271175

Funding Source: NSF of China

Award identifier / Grant number: 10901076

Funding Source: NSF of China

Award identifier / Grant number: 10931001

Funding Source: NSF of China

Award identifier / Grant number: 11101038

Funding Source: Linyi University

Award identifier / Grant number: AMEP

Funding Source: Key Laboratory of Mathematics and Complex System (Beijing Normal University), Ministry of Education, China


Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 2825–2851, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0064.

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