Year: 2025
Type: article
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 $T_Γ.$
Authors: Guantie Deng, Weiwei Wang
Institutions: Beijing Normal University, Civil Aviation University of China
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408464918