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Grand Lebesgue sequence spaces

  • Humberto Rafeiro EMAIL logo , Stefan Samko und Salaudin Umarkhadzhiev
Veröffentlicht/Copyright: 10. Mai 2018
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Abstract

We introduce grand Lebesgue sequence spaces and study various operators of harmonic analysis in these spaces, e.g., maximal, convolution, Hardy, Hilbert, and fractional operators, among others. Special attention is paid to fractional calculus, including the density of the discrete version of a Lizorkin sequence test space in vanishing grand spaces.

MSC 2010: 46A45; 42B05; 42B25

Dedicated to Professor V. Kokilashvili on the occasion of his 80th birthday


Funding statement: The first author was partially supported by Pontificia Universidad Javeriana under the research project with ID PPT: 7272. The second and third authors were partially supported by Grant 18-01-00094-a of Russian Foundation of Basic Research.

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Received: 2017-7-5
Revised: 2018-1-8
Accepted: 2018-1-10
Published Online: 2018-5-10
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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