Hardy space, kernel function and Saitoh's conjecture on products of planar domains

TL;DR

This paper investigates weighted Hardy spaces on product domains, analyzing their kernel functions, and proves product versions of Saitoh's conjecture, advancing understanding of function theory in complex analysis.

Contribution

It introduces and proves product versions of Saitoh's conjecture for weighted Hardy spaces on planar domain products, expanding classical results.

Findings

Established product versions of Saitoh's conjecture

Analyzed kernel functions for weighted Hardy spaces

Extended Hardy space theory to product domains

Abstract

In this article, we consider two classes of weighted Hardy spaces on products of planar domains and their corresponding kernel functions, and we prove product versions of Saitoh's conjecture related to the two classes of weighted Hardy spaces.