Brownian motion characterization of some Besov--Lipschitz spaces on domains
type: Item
instance of: scholarly article
title: Brownian motion characterization of some Besov--Lipschitz spaces on domains
zbMATH Open document ID: 1083.46016
DOI: 10.1007/BF02921862
author: H. Šikić
author: Mitchell H. Taibleson
published in: The Journal of Geometric Analysis
publication date: 2005-06-24T00:00:00Z
review text: Let \(\Omega\) be a bounded \(C^\infty\) domain in \(\mathbb R^n\). The subspaces \[ {}_{z} B^s_{pq} (\Omega) = \widetilde{B}^s_{pq} (\Omega) = \left\{ f \in B^s_{pq} (\mathbb R^n), \;\text{supp }f \subset \overline{\Omega} \right\} \] of the Besov spaces \(B^s_{pq} (\mathbb R^n)\) have been playing a role for decades in the theory of function spaces, in particular at present. It is well-known that the spaces \(B^s_{pq} (\mathbb R^n)\) can be characterized in terms of the Gauss--Weierstrass semigroup (thermic extension, Brownian motion in \(\mathbb{R}^n\)). It is the main aim of this paper to give a corresponding characterization of \({}_{z} B^s_{pq} (\Omega)\), restricted to \(1 \leq p,q \leq \infty\) and \(0<s<2\), in terms of Brownian motions on \(\Omega\).
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 2183026
zbMATH Keywords: Besov spaces
zbMATH Keywords: Brownian motion
MaRDI profile type: Publication
cites work: Q4039801
cites work: Q3276087
cites work: Q5725911
cites work: Q4173807
cites work: Q4890733
cites work: \(H^ p\) theory on a smooth domain in \(\mathbb{R}^ N\) and elliptic boundary value problems
cites work: Q3217388
cites work: Temperatures, Bessel Potentials and Lipschitz Spaces
cites work: Regular Elliptic Boundary Value Problems in Besov‐Triebel‐Lizorkin Spaces
cites work: Q4332829
cites work: On Excursions of Reflecting Brownian Motion
cites work: Q3766613
cites work: Some Theorems Concerning Brownian Motion
cites work: Q4223584
cites work: On Besov spaces and Sobolev spaces of generalized functions defined on a general region
cites work: Brownian potentials and Besov spaces
cites work: Q3048019
cites work: Q4114083
cites work: Intrinsic characterizations of distribution spaces on domains
cites work: On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
cites work: Multi-dimensional diffusion and the Markov process on the boundary
cites work: Q5640160
cites work: On the theory of harmonic functions of several variables
cites work: Q5341193
cites work: Q3336200
cites work: Q4003552
cites work: Q4836063
cites work: Intrinsic atomic characterizations of function spaces on domains
cites work: Q4039793
full work available at URL: https://doi.org/10.1007/bf02921862
OpenAlex ID: W2067800018
description: scientific article; zbMATH DE number 2183026