Imbedding theorems for Lipschitz spaces generated by the weak-\(L^p\) metric
type: Item
instance of: scholarly article
title: Imbedding theorems for Lipschitz spaces generated by the weak-\(L^p\) metric
zbMATH Open document ID: 0912.46029
author: Luca Brandolini
published in: Journal of Approximation Theory
publication date: 1999-05-03T00:00:00Z
review text: Given a normed space \(X\) of functions, one may define a modulus of smoothness with respect to \(X\) and consider a space \(\Lambda_X^\alpha(R^n)\) where this modulus satisfies certain growth conditions. Various imbedding theorems for such spaces are proved when \(X=L^{p,\infty}\) is a weak-\(L^p\) space. Since \(L^{p,\infty}\subseteq L^p\), some of these theorems generalize results from [\textit{R. A. DeVore} and \textit{G. G. Lorentz} [``Constructive approximation'' (1993; Zbl 0797.41016)]. The proofs are based on measure theoretic arguments, not on Fourier transforms. This allows to consider also \(p<1\).
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1214021
zbMATH Keywords: generalized Lipschitz space
zbMATH Keywords: generalized modulus of smoothness
zbMATH Keywords: weak \(L^p\) space
zbMATH Keywords: imbedding theorem
zbMATH Keywords: Fourier transforms
MaRDI profile type: Publication
full work available at URL: jath.1998.3183
OpenAlex ID: W2067871917
cites work: Q4039801
cites work: Q4273944
cites work: Q5577906
cites work: Q5640160
DOI: 10.1006/JATH.1998.3183
description: scientific article; zbMATH DE number 1214021