On first-order differential operators with Bohr-Neugebauer type property
type: Item
instance of: scholarly article
title: On first-order differential operators with Bohr-Neugebauer type property
zbMATH Open document ID: 0692.34063
DOI: 10.1155/S0161171289000608
author: Aribindi Satyanarayan Rao
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46446
review text: Let X be a Banach space; \(f\in L^ p_{loc}({\mathbb{R}},X)\) with \(p\in [1,+\infty [\) is said \(S^ p\)-bounded if \(| f|_{S^ p}\equiv \sup \{(\int^{t+1}_{t}| f(s)|^ p ds)^{1/p}:\quad t\in {\mathbb{R}}\}<+\infty.\) If f: \({\mathbb{R}}\to X\) is a continuously differentiable \(S^ 1\)-bounded function and \(f'\) is an \(S^ p\)-bounded function, then, if \(p=1\), f is bounded and, if \(p\in]1,+\infty [\), f is bounded and uniformly continuous. Let B: \(X\to X\) be a bounded linear operator such that any \(S^ 1\)-bounded u with \(u'-Bu=f\) is \(S^ 1\)-almost periodic for any (uniformly) almost-periodic X-valued function f. Then any \(S^ 1\)-bounded u such that \(u'-Bu=g\) is (uniformly) almost-periodic for any \(S^ 1\)-almost periodic continuous X-valued function g.
reviewed by: Gianfranco Bottaro
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34G99
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 4132633
zbMATH Keywords: \(S^ p\)-bounded function
MaRDI profile type: Publication
OpenAlex ID: W2066485505
description: scientific article; zbMATH DE number 4132633