Convergence and rate of approximation for linear integral operators in \(BV^{\varphi }\)-spaces in multidimensional setting
type: Item
instance of: scholarly article
title: Convergence and rate of approximation for linear integral operators in \(BV^{\varphi }\)-spaces in multidimensional setting
zbMATH Open document ID: 1154.26017
author: Laura Angeloni
author: Gianluca Vinti
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-11-06T00:00:00Z
review text: The authors introduce the space \(BV^{\varphi}(\mathbb{R}^N)\) of functions of bounded \(\varphi\)-variation in the sense of Tonelli and the \(\varphi\)-modulus of smoothness \(\omega_{\varphi}(f,\delta)\) for the functions \(f\) defined on \(\mathbb{R}^N\). For the linear convolution operators \[ (T_wf)(s)=\int_{\mathbb{R}^N}K_w(t)f(s-t)\,dt, \quad w>0, \quad s\in \mathbb{R}^N, \] under classical singularity assumptions on the family of kernels \(\{K_w\}_{w>0}\) the convergence results and rate of covergence results in the space \(BV^{\varphi}(\mathbb{R}^N)\) or in some of its subspaces are established.
reviewed by: Boris Golubov
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 5362159
zbMATH Keywords: linear convolution integral operators
zbMATH Keywords: multidimensional \(\varphi\)-variation
zbMATH Keywords: rate of approximation
zbMATH Keywords: Lipschitz classes
zbMATH Keywords: \(\varphi\)-modulus of smoothness
zbMATH Keywords: higher order of approximation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.08.029
OpenAlex ID: W2040246333
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DOI: 10.1016/J.JMAA.2008.08.029
description: scientific article; zbMATH DE number 5362159