On convolution operators in the spaces of almost periodic functions and \(L^p\) spaces
type: Item
instance of: scholarly article
title: On convolution operators in the spaces of almost periodic functions and \(L^p\) spaces
zbMATH Open document ID: 0972.47036
DOI: 10.4171/ZAA/955
author: Giordano Bruno
author: Alexander Pankov
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2000-11-16T00:00:00Z
full work available at URL: https://eudml.org/doc/48948
review text: The authors consider convolution operators generated by \(L^1\) functions in \(L^p\) spaces and in the spaces of Bohr, Stepanov and Besicovich of almost periodic functions. They prove that if such an operator is invertible in one of these spaces, then it is invertible in all the spaces. Next, they also prove that convolution operators have identical norms in each of two members of the couples: \(L^p\) and \(B^p\), \(BS^p\) and \(S^p\), \(C_b\) and CAP.
reviewed by: Viorel Iftimie
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1501861
zbMATH Keywords: convolution operators
zbMATH Keywords: spaces of Bohr, Stepanov and Besicovich of almost periodic functions
MaRDI profile type: Publication
cites work: Q4843564
cites work: Q3254057
cites work: Q3125681
cites work: Q4356303
cites work: Q3905855
cites work: Q3999242
cites work: Almost periodic functions, Bohr compactification, and differential equations
cites work: ALMOST PERIODIC FUNCTIONS AND PARTIAL DIFFERENTIAL OPERATORS
cites work: Theorems on the coincidence of the spectra of pseudodifferential almost-periodic operators in the spaces \(L^2(\mathbb R^n)\) and \(B^2(\mathbb R^n)\)
cites work: Q5640160
OpenAlex ID: W2020213672
description: scientific article; zbMATH DE number 1501861