Integral Representations in Weighted Bergman Spaces on the Tube Domains

TL;DR

This paper develops Laplace transform representations for functions in weighted Bergman spaces on tube domains and derives a weighted edge-of-the-wedge theorem as a key result.

Contribution

It introduces new Laplace transform representations and a weighted edge-of-the-wedge theorem for functions in weighted Bergman spaces on tube domains.

Findings

Laplace transform representations for weighted Bergman space functions

A weighted edge-of-the-wedge theorem is established

New analytical tools for tube domain function theory

Abstract

Herein, the Laplace transform representations for functions of weighted holomorphic Bergman spaces on the tube domains are developed. Then a weighted version of the edge-of-the-wedge theorem is derived as a byproduct of the main results.