Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions.
type: Item
instance of: scholarly article
title: Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions.
zbMATH Open document ID: 1036.46024
DOI: 10.4171/RMI/329
author: Herbert Koch
author: Winfried Sickel
published in: Revista Matemática Iberoamericana
publication date: 2003-09-25T00:00:00Z
full work available at URL: https://eudml.org/doc/39696
review text: Let \(B^s_{pq} (\mathbb{R}^n)\) with \(1 \leq p,q \leq \infty\) and \(s \in \mathbb{R}\) be the well-known Besov spaces in Euclidean \(n\)-space \(\mathbb{R}^n\). A function \(m \in L_\infty (\mathbb{R}^n)\) is said to be a pointwise multiplier for \(B^s_{pq} (\mathbb{R}^n)\) if \( f \mapsto mf\) is a bounded map in \(B^s_{pq} (\mathbb{R}^n)\). The characterisation of the collection of all pointwise multipliers, denoted by \(M(B^s_{pq})\), has attracted a lot of attention for decades. The present paper deals with the characterisations of \(M(B^0_{\infty, \infty})\) (Theorem 4) and \(M(B^0_{\infty, 1} )\) (Theorem 5) which are especially complicated. Applications to regularity assertions for elliptic partial differential equations are given.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 1931492
zbMATH Keywords: Besov spaces
zbMATH Keywords: pointwise multipliers
MaRDI profile type: Publication
cites work: Fonctions qui opèrent sur les espaces de Besov et de Triebel. (Functions which operate on Besov and Triebel spaces.)
cites work: Fonctions qui opèrent sur les espaces de Sobolev. (Functions that operate on Sobolev spaces)
cites work: Gradient estimates for variable coefficient parabolic equations and singular perturbation problems
cites work: On the Spaces of T<scp>riebel‐</scp>L<scp>izorkin</scp> Type: Pointwise Multipliers and Spaces on Domains
cites work: A discrete transform and decompositions of distribution spaces
cites work: Q4000004
cites work: A local version of real Hardy spaces
cites work: Q3700281
cites work: Q3711141
cites work: The Green function for uniformly elliptic equations
cites work: On functions with conditions on the mean oscillation
cites work: Pointwise Multiplication of Besov and Triebel‐Lizorkin Spaces
cites work: Some remarks on Triebel spaces
cites work: On the Boundedness and Compactness of Nonregular Pseudo‐Differential Operators
cites work: Nonregular pseudo-differential operators
cites work: Q3788519
cites work: Q4272018
cites work: Q4129323
cites work: Q4893982
cites work: On a theorem of Bui, Paluszyński, and Taibleson
cites work: Remarks on singular convolution operators
cites work: On pointwise multipliers for \(F_{p,q}^s (\mathbb{R}^n)\) in case \(\sigma_{p,q}< s< n/p\)
cites work: Hölder inequalities and sharp embeddings in function spaces of \(B_{pq}^ s\) and \(F_{pq}^ s\) type
cites work: Bounded Toeplitz Operators on H 1 and Applications of the Duality Between H 1 and the Functions of Bounded Mean Oscillation
cites work: Q5522602
Recommended article: Pointwise multipliers for Besov spaces of dominating mixed smoothness. II
Recommended article: Q3817159
Recommended article: Pointwise multipliers for Sobolev and Besov spaces of dominating mixed smoothness
Recommended article: Pointwise Multiplication of Besov and Triebel‐Lizorkin Spaces
Recommended article: Q4592962
Recommended article: Q5489490
Recommended article: On the pointwise multiplication in Besov and Lizorkin-Triebel spaces
Recommended article: Pointwise multipliers of Besov spaces on Carnot-Carathéodory spaces
Recommended article: Pointwise multipliers and decomposition theorems in analytic Besov spaces
Recommended article: Q4810762
description: scientific article; zbMATH DE number 1931492