A characterization of Besov classes in terms of a new modulus of continuity
type: Item
instance of: scholarly article
title: A characterization of Besov classes in terms of a new modulus of continuity
zbMATH Open document ID: 1393.46026
DOI: 10.1134/S1064562417060187
author: Egor D. Kosov
published in: Doklady Mathematics
publication date: 2018-03-28T00:00:00Z
review text: It is well known that the classical Besov spaces \(B^\alpha_{p,\theta} (\mathbb R^n)\) with \(0<\alpha<1\), \(1\leq p \leq \infty\), \(1\leq \theta \leq \infty\), can be characterized in tems of the modulus of continuity \[ \omega_p (f,r) = \sup_{| h| \leq r} \| f(\cdot-h) - f(\cdot) \mid L_p (\mathbb R^n) \|. \] The author introduces some new moduli of continuity incorporating first derivatives (for example as the divergence of related vector-functions). It is the main aim of the paper to show that the above Besov spaces can be characterized in terms of these new moduli of continuity and that some new properties can be proved, including modifications of the Gagliardo-Nirenberg inequalities.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 6854407
zbMATH Keywords: Besov spaces
zbMATH Keywords: modulus of continuity
zbMATH Keywords: Gagliardo-Nirenberg inequalities
MaRDI profile type: Publication
cites work: Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures
cites work: Q4003552
cites work: Q4173807
cites work: Q4064526
cites work: Q5607484
cites work: Gagliardo-Nirenberg inequalities
cites work: THE IMBEDDING OF CERTAIN FUNCTION CLASSESHpω
cites work: IMBEDDING THEOREMS AND RELATIONS BETWEEN BEST APPROXIMATIONS (MODULI OF CONTINUITY) IN DIFFERENT METRICS
cites work: ON IMBEDDING IN CLASSES $ \phi(L)$
cites work: ESTIMATES OF REARRANGEMENTS AND IMBEDDING THEOREMS
cites work: Rearrangements of functions and embedding theorems
full work available at URL: s1064562417060187
OpenAlex ID: W2782361252
Recommended article: A new approach to Nikolskii-Besov classes
Recommended article: A new characterization of Besov spaces on the real line
Recommended article: Q3123610
Recommended article: Besov classes on finite and infinite dimensional spaces
Recommended article: Continuous characterization of the Besov spaces of variable smoothness and integrability
Recommended article: Besov classes on infinite-dimensional spaces
Recommended article: Generalization of a theorem on Besov-Nikol'skiĭ classes
Recommended article: Q4726867
Recommended article: Q4397859
Recommended article: A Beurling-Helson type theorem for modulation spaces
description: scientific article; zbMATH DE number 6854407