Blaschke Products and Zero Sets in Weighted Dirichlet Spaces

被引：2

作者：

Idrissi, H. Bahajji-El ^{[1
]}

El-Fallah, O. ^{[1
]}

机构：

[1] Mohammed 5 Univ Rabat, Lab Math Anal & Applicat, Fac Sci, BP 1014, Rabat, Morocco

来源：

POTENTIAL ANALYSIS | 2020年 / 53卷 / 04期

关键词：

Blaschke product; Dirichlet space; Capacity; BOUNDARY-BEHAVIOR; INNER FUNCTIONS; BERGMAN SPACES; DERIVATIVES;

D O I：

10.1007/s11118-019-09807-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we deal with superharmonically weighted Dirichlet spaces D-w. First, we prove that the classical Dirichlet space is the largest, among all these spaces, which contains no infinite Blaschke product. Next, we give new sufficient conditions on a Blaschke sequence to be a zero set for D-w. Our conditions improve Shapiro-Shields condition for D-alpha, when alpha is an element of (0, 1).

引用

页码：1299 / 1316

页数：18

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