Abstract

This article continues the study of the Hadamard–Bergman operators in the unit disk of the complex plane. These operators arose as a natural generalization of orthogonal projections and represent an integral realization of multiplier operators. However, the study of operators in integral form offers a number of advantages in the context of the application of the theory of integral operators as well as in the study of certain function spaces such as holomorphic Hölder functions to which the multiplier theory does not apply. As a main result, we prove boundedness theorems for the Hadamard–Bergman operators and variable Hadamard–Bergman operators using the technique of operators with homogeneous kernels earlier developed in real analysis.

中文翻译：

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Hadamard-Bergman 和变量 Hadamard-Bergman 卷积算子的有界性

摘要

本文继续研究复平面单位圆盘中的Hadamard-Bergman算子。这些算子是作为正交投影的自然推广而出现的，代表了乘法算子的完整实现。然而，在积分算子理论的应用以及乘子理论不适用的某些函数空间（例如全纯 Hölder 函数）的研究中，积分形式算子的研究提供了许多优点。作为主要结果，我们使用早期实分析中开发的齐次核算子技术证明了 Hadamard-Bergman 算子和变量 Hadamard-Bergman 算子的有界定理。