TY - JOUR
T1 - Distributional Boundary Values of Holomorphic Functions on Tubular Domains
AU - Deng , Guantie
AU - Wang , Weiwei
JO - Analysis in Theory and Applications
VL - 1
SP - 35
EP - 51
PY - 2025
DA - 2025/04
SN - 41
DO - http://doi.org/10.4208/ata.OA-2022-0017
UR - https://global-sci.org/intro/article_detail/ata/23957.html
KW - The weighted Hardy space, distributional boundary values, tubular domains.
AB - <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>