Hilbert Spaces Contractively Contained in Weighted Bergman Spaces on the Unit Disk
Functional Analysis
2018-11-16 v2
Abstract
Sub-Bergman Hilbert spaces are analogues of de Branges-Rovnyak spaces in the Bergman space setting. They are reproducing kernel Hilbert spaces contractively contained in the Bergman space of the unit disk. K. Zhu analyzed sub-Bergman Hilbert spaces associated with finite Blaschke products, and proved that they are norm equivalent to the Hardy space. Later S. Sultanic found a different proof of Zhu's result, which works in weighted Bergman space settings as well. In this paper, we give a new approach to this problem and obtain a stronger result. Our method relies on the theory of reproducing kernel Hilbert spaces.
Keywords
Cite
@article{arxiv.1807.08366,
title = {Hilbert Spaces Contractively Contained in Weighted Bergman Spaces on the Unit Disk},
author = {Cheng Chu},
journal= {arXiv preprint arXiv:1807.08366},
year = {2018}
}