On Unique Minimal $$\boldsymbol{L}^{\boldsymbol{p}}$$ -Norm Harmonic or Holomorphic Function Which Takes Given Value in a Fixed Point

Pub Date : 2024-07-09 DOI:10.3103/s1068362324700134

T. Ł. Żynda

引用次数: 0

Abstract

First, it will be shown that Banach spaces $V$ of harmonic or holomorphic functions with $L^{p}$ norm satisfy minimal norm property, i.e., in any set

$$V_{z,c}:=\{f\in V\>|\>f(z)=c\},$$

if nonempty, there is exactly one element with minimal norm. Later, it will be proved that this element depends continuously on a deformation of a norm and on an increasing sequence of domains in a precisely defined sense.

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On Unique Minimal $$\boldsymbol{L}^{\boldsymbol{p}}$ -Norm Harmonic or Holomorphic Function Which Takes Given Value in a Fixed Point

摘要首先，我们将证明具有 $L^{p}$ 准则的谐函数或全形函数的巴拿赫空间 $V$ 满足最小准则性质，即在任意集合$$V_{z,c}:=\{f\in V\>|\>f(z)=c\}, $$如果非空，则正好有一个元素具有最小准则。稍后，我们将证明这个元素在精确定义的意义上连续依赖于规范的变形和域的递增序列。

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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