Dirichlet Spaces with Superharmonic Weights and de Branges-Rovnyak Spaces

被引：15

作者：

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

Kellay, K. ^{[2
]}

Klaja, H. ^{[3
]}

Mashreghi, J. ^{[3
]}

Ransford, T. ^{[3
]}

机构：

[1] Univ Mohammed 5, Lab Anal & Applicat URAC 03, BP 1014, Rabat, Morocco

[2] Univ Bordeaux, Inst Math Bordeaux, 351 Cours Liberat, F-33405 Talence, France

[3] Univ Laval, Dept Math & Stat, 1045 Ave Med, Quebec City, PQ G1V 0A6, Canada

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2016年 / 10卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Dirichlet space; Superharmonic; de Branges-Rovnyak space;

D O I：

10.1007/s11785-015-0474-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Dirichlet spaces with superharmonic weights. This class contains both the harmonic weights and the power weights. Our main result is a characterization of the Dirichlet spaces with superharmonic weights that can be identified as de Branges-Rovnyak spaces. As an application, we obtain the dilation inequality D-omega(fr) <= 2r/1 + r D-omega(f) (0 <= r < 1), where D-omega denotes the Dirichlet integral with superharmonic weight., and fr (z) := f (rz) is the r - dilation of the holomorphic function f.

引用

页码：97 / 107

页数：11

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