Distributional Boundary Values of Holomorphic Functions on Tubular Domains
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 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′Lp(Rn), where 1≤p≤2. In addition, we will also study the inverse result, in which we will prove that f(z) is holomorphic on TΓ.
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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.
Author Details
Guantie Deng Email
Weiwei Wang Email