有径向权重的伯格曼空间的科伦布伦原理

IF 0.6 4区数学 Q3 MATHEMATICS

Computational Methods and Function Theory Pub Date : 2024-05-18 DOI:10.1007/s40315-024-00543-6

Iason Efraimidis, Adrián Llinares, Dragan Vukotić

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引用次数: 0

摘要

我们证明，在 \(1\le p<\infty \)情况下，Korenblum 最大（支配）原则对于具有任意（非负且可整）径向权重 w 的加权伯格曼空间 \(A^p_w\)是有效的。我们还注意到，在每一个加权伯格曼空间中，该原则成立的所有半径的上集都严格小于1。在温和的附加假设（(liminf _{r\rightarrow 0^+} w(r)>0\)）下，我们证明只要\(0<p<1\)，原则就失效。

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Korenblum’s Principle for Bergman Spaces with Radial Weights

We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces \(A^p_w\) with arbitrary (non-negative and integrable) radial weights w in the case \(1\le p<\infty \). We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption \(\liminf _{r\rightarrow 0^+} w(r)>0\), we show that the principle fails whenever \(0<p<1\).

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来源期刊

Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.