Hausdorff operators on Morrey-type spaces

V. Burenkov; E. Liflyand

doi:10.1215/21562261-2019-0035

Abstract

After 2000, interest in the Hausdorff operators grew, first in the sense of the variety of spaces on which these operators were considered. Here we give conditions ensuring the boundedness of such operators on Morrey-type spaces. The sharpness of the obtained results is studied, and classes of the Hausdorff operators are described for which the necessary and sufficient conditions coincide.

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V. Burenkov. E. Liflyand. "Hausdorff operators on Morrey-type spaces." Kyoto J. Math. 60 (1) 93 - 106, April 2020. https://doi.org/10.1215/21562261-2019-0035

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Received: 7 June 2016; Revised: 10 January 2017; Accepted: 14 September 2017; Published: April 2020

First available in Project Euclid: 13 September 2019

zbMATH: 07194829

MathSciNet: MR4065182

Digital Object Identifier: 10.1215/21562261-2019-0035

Subjects:

Primary: 47B38

Secondary: 42B10 , 46E30

Keywords: global Morrey-type space , Hausdorff operator , local Morrey-type space , Morrey space

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