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Abstract
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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
spaces if and only if the symbol functions of the commutators belong to
spaces (the
central
closure of
).
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Keywords
Hardy operator, commutator, compactness, BMO
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Mathematical Subject Classification 2010
Primary: 42B25, 47B47, 47G10
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Milestones
Received: 24 July 2018
Revised: 20 December 2019
Accepted: 21 March 2020
Published: 8 August 2020
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