The Cauchy Transform on the Bergman–Dirichlet SpacesThe Cauchy Transform on the Bergman–Dirichlet SpacesA. Benahmadi et al.

被引：0

作者：

Abdelhadi Benahmadi ^{[1
]}

Abdellatif Elkachkouri ^{[1
]}

Allal Ghanmi ^{[1
]}

机构：

[1] Mohammed V University in Rabat,Analysis, P.D.E & Spectral Geometry, Lab M.I.A.

来源：

Mediterranean Journal of Mathematics | 2025年 / 22卷 / 4期

关键词：

Cauchy transform; Bergman spaces; Dirichlet spaces; Bergman–Dirichlet spaces; reproducing kernel; bi-analytic functions; Primary 30E20; 30H20;

D O I：

10.1007/s00009-025-02862-x

中图分类号：

学科分类号：

摘要：

We show that the range of the Cauchy transform on the classical Bergman space is the reproducing kernel Hilbert space of functions in the bi-analytic Dirichlet space subject to a first-order differential equation. The closed formula of its reproducing kernel is given explicitly. Our investigation includes an explicit characterization of the range of the weighted Cauchy transform on the weighted Bergman–Dirichlet spaces, extending Dyn’kin’s result showing that the single-valued functions in the Dirichlet space vanishing at the origin are the Cauchy transform of some functions in the Bergman space of anti-holomorphic functions.

引用