Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups equipped with Haar measure

Maria Rosaria Formica; Eugeny Ostrovsky; Leonid Sirota

doi:10.1002/mana.201900181

Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups equipped with Haar measure

Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota

Department of Mathematics

University of Naples Parthenope

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove that the Grand Lebesgue Space built on a unimodular locally compact topological group, equipped with bi-invariant Haar measure, forms a Banach algebra relative to the convolution.

Original language	English
Pages (from-to)	1702-1714
Number of pages	13
Journal	Mathematische Nachrichten
Volume	294
Issue number	9
DOIs	https://doi.org/10.1002/mana.201900181
State	Published - Sep 2021

Bibliographical note

Publisher Copyright:
© 2021 Wiley-VCH GmbH

Funding

The first named author has been partially supported by the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Università degli Studi di Napoli Parthenope through the project “sostegno alla Ricerca individuale”.

Funders	Funder number
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Università degli Studi di Napoli Parthenope

Keywords

Grand Lebesgue Spaces
Haar measure
Lebesgue–Riesz space
Young inequality
beta-function
convolution
locally compact topological groups
modulus of continuity
unimodular group

Access to Document

10.1002/mana.201900181

Cite this

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abstract = "We prove that the Grand Lebesgue Space built on a unimodular locally compact topological group, equipped with bi-invariant Haar measure, forms a Banach algebra relative to the convolution.",

keywords = "Grand Lebesgue Spaces, Haar measure, Lebesgue–Riesz space, Young inequality, beta-function, convolution, locally compact topological groups, modulus of continuity, unimodular group",

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AU - Sirota, Leonid

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KW - Lebesgue–Riesz space

KW - Young inequality

KW - beta-function

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KW - locally compact topological groups

KW - modulus of continuity

KW - unimodular group

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Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups equipped with Haar measure

Abstract

Bibliographical note

Funding

Keywords

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