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arXiv · 2409.20265

BMO on Weighted Bergman Spaces over Tubular Domains

Jiaqing Ding·Haichou Li·Zhiyuan Fu·Yanhui Zhang
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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.

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Jiaqing Ding, Haichou Li, Zhiyuan Fu, Yanhui Zhang. 2024-09-30. BMO on Weighted Bergman Spaces over Tubular Domains. https://arxiv.org/abs/2409.20265

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