Properties of the voice transform of the Blaschke group and connections with atomic decomposition results in the weighted Bergman spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Pap, Margit^1,2 

[1] Univ Pecs, H-7634 Pecs, Hungary

[2] Univ Vienna, Fac Math, NuHAG, A-1090 Vienna, Austria

关键词: Voice transform;    Weighted Bergman spaces;    Atomic decompositions;   

DOI  :  10.1016/j.jmaa.2011.11.060

来源: Elsevier

【 摘 要 】

Feichtinger and Grochenig described a unified approach to atomic decomposition through integrable group representations in Banach spaces. Studying the properties of a special voice transform of the Blascke group, outlined by the general theory developed by Feichtinger and Grochenig, we obtain that every function from the minimal Mobius invariant space will generate an atomic decomposition in the weighted Bergman spaces. In the unified approach of the atomic decomposition a useful tool is the Q-density, the V-separated property and the bounded uniform partitions of the unity of the locally compact group. Using the hyperbolic metric we can describe the Q-density from right, and the separation from right in the Blaschke group. Using this we can give an example of bounded uniform partitions of the unity from right. In the general theory of atomic decomposition it is used the Q-density from the left, this is the reason why we will make a small modification in the discretizing operator which corresponds to the Q-density from the right in order to obtain atomic decomposition in the weighted Bergman spaces. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free