Minimal $L^2$ integrals for the Hardy spaces and the Bergman spaces

Qi'an Guan; Zheng Yuan

Minimal $L^2$ integrals for the Hardy spaces and the Bergman spaces

Complex Variables 2023-04-05 v1

Authors: Qi'an Guan , Zheng Yuan

Abstract

In this article, we consider the minimal $L^2$ integrals for the Hardy spaces and the Bergman spaces, and we present some relations between them, which can be regarded as the solutions of the finite points versions of Saitoh's conjecture for conjugate Hardy kernels. As applications, we give optimal $L^2$ extension theorems for the Hardy spaces, and characterizations for the holding of the equality in the optimal $L^2$ extension theorems.

Keywords

minimal L^2 integrals Hardy spaces Bergman spaces Saitoh's conjecture L^2 extension theorem conjugate Hardy kernels

Cite

@article{arxiv.2304.01630,
  title  = {Minimal $L^2$ integrals for the Hardy spaces and the Bergman spaces},
  author = {Qi'an Guan and Zheng Yuan},
  journal= {arXiv preprint arXiv:2304.01630},
  year   = {2023}
}

Comments

50 pages, all comments are welcome. arXiv admin note: substantial text overlap with arXiv:2210.14579

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