Boundedness criteria for the Hardy-Steklov operator expressed in terms of a fairway function
type: Item
instance of: scholarly article
title: Boundedness criteria for the Hardy-Steklov operator expressed in terms of a fairway function
zbMATH Open document ID: 1338.47056
DOI: 10.1134/S1064562415020246
published in: Doklady Mathematics
publication date: 2015-08-21T00:00:00Z
review text: Let \(s\in\mathbb R\) and \(g\), \(\varphi\), \(\psi\) be nonnegative functions on the half-axis. If there exists a function \(\sigma(x)\) with values between \(\varphi(x)\) and \(\psi(x)\) such that \[ \int_{\varphi(x)}^{\sigma(x)}g^{s}(x)\,dy = \int_{\sigma(x)}^{\psi(x)}g^{s}(x)\,dy, \quad x>0, \] it is called a fairway function. The Hardy-Steklov operator is defined on the functions on the half-axis as follows \[ ({\mathcal H}f)(x) = \int_{a(x)}^{b(x)}f(y)\,dy, \quad x>0. \] In this paper, using the method of fairway functions, two-sided estimates are given for the norms of these operators acting from one weighted \(L_{p}\)-space on the half-space into another such space. The estimates depend only on these spaces and the functions \(a(x), b(x)\).
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 6474462
zbMATH Keywords: Hardy-Steklov operator
zbMATH Keywords: boundedness
zbMATH Keywords: norms
zbMATH Keywords: weighted \(L_{p}\)-space
zbMATH Keywords: fairway function
author: E. P. Ushakova
MaRDI profile type: Publication
cites work: Q4386417
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full work available at URL: s1064562415020246
OpenAlex ID: W860317500
description: scientific article; zbMATH DE number 6474462