Vol. 307, No. 1, 2020

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On the compactness of commutators of Hardy operators

Shaoguang Shi, Zunwei Fu and Shanzhen Lu

Vol. 307 (2020), No. 1, 239–256
Abstract

We focus on the need for the compactness characterizations of the commutators of Hardy operators. More precisely, we prove that the commutators of Hardy operators, including the fractional Hardy operator, are compact operators on Lp(n)(1 < p < ) spaces if and only if the symbol functions of the commutators belong to CVMO(n) spaces (the central BMO(n) closure of Cc(n)).

Keywords
Hardy operator, commutator, compactness, BMO
Mathematical Subject Classification 2010
Primary: 42B25, 47B47, 47G10
Milestones
Received: 24 July 2018
Revised: 20 December 2019
Accepted: 21 March 2020
Published: 8 August 2020
Authors
Shaoguang Shi
School of Science, Department of Mathematics
Linyi University
Linyi
China
Zunwei Fu
Department of Mathematics
Linyi University
Linyi
China
School of Mathematical Sciences
Qufu Normal University
Qufu
China
Shanzhen Lu
School of Mathematical Sciences
Beijing Normal University
Beijing
China