## Abstract and Applied Analysis

### Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type

#### Abstract

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 μ 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 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 265378, 13 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425049900

Digital Object Identifier
doi:10.1155/2014/265378

Mathematical Reviews number (MathSciNet)
MR3293817

Zentralblatt MATH identifier
07022049

#### Citation

Chen, Chuang; Li, Ji; Liao, Fanghui. Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type. Abstr. Appl. Anal. 2014 (2014), Article ID 265378, 13 pages. doi:10.1155/2014/265378. https://projecteuclid.org/euclid.aaa/1425049900