Weighted versions of Saitoh's conjecture in fibration cases

TL;DR

This paper introduces generalized Hardy spaces on fibrations of planar domains, studies their kernel functions, and proves weighted versions of Saitoh's conjecture specific to these fibrations.

Contribution

It extends Saitoh's conjecture to weighted cases within the context of fibrations of planar domains, providing new theoretical insights.

Findings

Established weighted Saitoh's conjecture for fibrations

Analyzed kernel functions on generalized Hardy spaces

Extended classical results to fibration settings

Abstract

In this article, we introduce some generalized Hardy spaces on fibrations of planar domains and fibrations of products of planar domains. We consider the kernel functions on these spaces, and we prove some weighted versions of Saitoh's conjecture in fibration cases.