Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-11-06 DOI:10.3390/axioms12111036

Richard D. Carmichael

引用次数: 0

Abstract

Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p<2, if the boundary value is in the vector-valued Lp,1≤p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2≤p≤∞. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1≤p≤∞.

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边值为向量值调质分布的向量值解析函数

Cn中已知具有向量值缓变分布边值的向量值解析函数在Hardy空间Hp中，1≤p<2，如果边值在向量值Lp中，1≤p<2，函数。本文的分析推广了前人研究2≤p≤∞情况的分析。由此，通过对本文结果的补充，证明了所考虑的问题对所有p,1≤p≤∞都成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.