Year: 2025
Author: Guantie Deng, Weiwei Wang
Analysis in Theory and Applications, Vol. 41 (2025), Iss. 1 : pp. 35–51
Abstract
The main purpose of this paper is to establish the distributional boundary values of functions in the weighted Hardy space, which improves the results of Carmichael in [4] and [8], where the weight function is linear. As our main result, we will prove that $f(z)$ in $H(ψ, Γ)$ has the $\mathcal{Z}'$ boundary value and can be expressed by the inverse Fourier transform of a distribution. Next, we will establish the $S'$ boundary value under stronger assumptions and give more precise expression if $f(z)$ also converges to $U ∈ D'_{L^p}(\mathbb{R}^n),$ where $1 ≤ p ≤ 2.$ In addition, we will also study the inverse result, in which we will prove that $f(z)$ is holomorphic on $T_Γ.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2022-0017
Analysis in Theory and Applications, Vol. 41 (2025), Iss. 1 : pp. 35–51
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: The weighted Hardy space distributional boundary values tubular domains.