Complex interpolation of Besov-type spaces on domains
type: Item
instance of: scholarly article
title: Complex interpolation of Besov-type spaces on domains
zbMATH Open document ID: 1480.46034
DOI: 10.4171/ZAA/1687
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2021-07-19T00:00:00Z
review text: Summary: Let \(\Omega\subset\mathbb{R}^d\) \((d\geq 2)\) be a bounded Lipschitz domain. In this article, the author mainly studies complex interpolation of Besov-type spaces on the domain \(\Omega\), namely, we investigate the interpolation \[ [B_{p_0,q_0}^{s_0,\tau_0}(\Omega),B_{p_1,q_1}^{s_1,\tau_1}(\Omega)]_\Theta=B_{p,q}^{\diamond s,\tau}(\Omega) \] under certain conditions on the parameters, where \(B_{p,q}^{\diamond s,\tau}(\Omega)\) denotes the so-called diamond space associated with the Besov-type space. To this end, we first establish the equivalent characterization of the diamond space \(B_{p,q}^{\diamond s,\tau}(\mathbb{R}^d)\) in terms of Littlewood-Paley decomposition and differences. Via some examples, we also show that this interpolation result does not hold under some other assumptions on the parameters or when \(\Omega=\mathbb{R}^d\).
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7372684
zbMATH Keywords: Besov-type space
zbMATH Keywords: diamond space
zbMATH Keywords: extension operator
zbMATH Keywords: Lipschitz domains
zbMATH Keywords: complex interpolation
author: Ciqiang Zhuo
MaRDI profile type: Publication
cites work: Q4112938
cites work: Characterizations of weighted Besov and Triebel-Lizorkin spaces via temperatures
cites work: Characterization of the Besov-Lipschitz and Triebel-Lizorkin spaces. The case \(q<1\)
cites work: Q4890733
cites work: Intermediate spaces and interpolation, the complex method
cites work: Complex interpolation of certain closed subspaces of generalized Morrey spaces
cites work: Complex interpolation of smoothness Morrey subspaces
cites work: Complex interpolation of smoothness Triebel-Lizorkin-Morrey spaces
cites work: Interpolation of generalized Morrey spaces
cites work: Calderón's first and second complex interpolations of closed subspaces of Morrey spaces
cites work: Complex interpolation of vanishing Morrey spaces
cites work: Complex interpolation of various subspaces of Morrey spaces
cites work: BESOV-TYPE SPACES AND DIFFERENCES
cites work: Q5448226
cites work: Q3955929
cites work: Multipliers and Morrey spaces
cites work: Erratum to: ``Multipliers and Morrey spaces''
cites work: New characterizations of Besov-Triebel-Lizorkin-Hausdorff spaces including coorbits and wavelets
cites work: A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces
cites work: Interpolation of Morrey spaces on metric measure spaces
cites work: On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
cites work: Decompositions of Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces
cites work: Q4051120
cites work: Interpolation of linear operators in spaces of measurable functions
cites work: Smoothness spaces related to Morrey spaces: a survey. I
cites work: Complex interpolation of weighted Besov and Lizorkin-Triebel spaces
cites work: Some properties of Morrey type Besov-Triebel spaces
cites work: Q4169289
cites work: Q3336200
cites work: Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
cites work: Function spaces and wavelets on domains
cites work: Equivalent quasi-norms of Besov-Triebel-Lizorkin-type spaces via derivatives
cites work: Complex interpolation on Besov-type and Triebel-Lizorkin-type spaces
cites work: Embedding properties of Besov-type spaces
cites work: Morrey and Campanato meet Besov, Lizorkin and Triebel
cites work: Interpolation of Morrey-Campanato and related smoothness spaces
cites work: Complex interpolation of Lizorkin-Triebel-Morrey spaces on domains
cites work: Characterizations of Besov-Type and Triebel–Lizorkin–Type Spaces via Averages on Balls
full work available at URL: https://doi.org/10.4171/zaa/1687
OpenAlex ID: W3175124724
description: scientific article; zbMATH DE number 7372684