BMO on Weighted Bergman Spaces over Tubular Domains
Complex Variables
2024-10-01 v1 Functional Analysis
Abstract
In this paper, we characterize Bounded Mean Oscillation (BMO) and establish their connection with Hankel operators on weighted Bergman spaces over tubular domains. By utilizing the space BMO, we provide a new characterization of Bloch spaces on tubular domains. Next, we define a modified projection operator and prove its boundedness. Furthermore, we introduce differential operators and demonstrate that these operators belong to Lebesgue spaces on tubular domains. Finally, we establish an integral representation for Bergman functions using these differential operators.
Cite
@article{arxiv.2409.20265,
title = {BMO on Weighted Bergman Spaces over Tubular Domains},
author = {Jiaqing Ding and Haichou Li and Zhiyuan Fu and Yanhui Zhang},
journal= {arXiv preprint arXiv:2409.20265},
year = {2024}
}