Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type

Chuang Chen, Ji Li and Fanghui Liao

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let (X, d, μ) 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 μ satisfies only the doubling property. Adapting the recently developed randomized dyadic structures of X and applying orthonormal bases of L2(X) constructed recently by Auscher and Hytönen, 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 μ to the full generality of the theory of these function spaces.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/265378

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:265378

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().