Some function spaces via orthonormal bases on spaces of homogeneous type
type: Item
instance of: scholarly article
title: Some function spaces via orthonormal bases on spaces of homogeneous type
zbMATH Open document ID: 1468.42024
DOI: 10.1155/2014/265378
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Let \((X, d, \mu)\) be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metric \(d\) may have no regularity and the measure \(\mu\) satisfies only the doubling property. Adapting the recently developed randomized dyadic structures of \(X\) and applying orthonormal bases of \(L^2(X)\) constructed recently by \textit{P. Auscher} and \textit{T. Hytönen} [Appl. Comput. Harmon. Anal. 34, No. 2, 266--296 (2013; Zbl 1261.42057)], we develop the Besov and Triebel-Lizorkin spaces on such a general setting. In this paper, we establish the wavelet characterizations and provide the dualities for these spaces. The results in this paper extend earlier related results with additional assumptions on the quasi-metric \(d\) and the measure \(\mu\) to the full generality of the theory of these function spaces.
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 7022049
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/265378
OpenAlex ID: W2154538530
Wikidata QID: Q59037339
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description: scientific article; zbMATH DE number 7022049