@Article{ATA-41-35,
author = {Deng , Guantie and Wang , Weiwei},
title = {Distributional Boundary Values of Holomorphic Functions on Tubular Domains},
journal = {Analysis in Theory and Applications},
year = {2025},
volume = {41},
number = {1},
pages = {35--51},
abstract = {<p style="text-align: justify;">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 $\mathcal{Z}&#39;$ boundary value and can be expressed by the
inverse Fourier transform of a distribution. Next, we will establish the $S&#39;$ boundary
value under stronger assumptions and give more precise expression if $f(z)$ also converges to $U ∈ D&#39;_{L^p}(\mathbb{R}^n),$ where $1 ≤ p ≤ 2.$ In addition, we will also study the inverse
result, in which we will prove that $f(z)$ is holomorphic on $T_Γ.$</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2022-0017},
url = {http://global-sci.org/intro/article_detail/ata/23957.html}
}