Boundedness of Hadamard–Bergman and Variable Hadamard–Bergman Convolution Operators

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-03-12 DOI:10.1134/s0001434623110160

A. Karapetyants, E. Morales

引用次数: 0

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.

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哈达玛-伯格曼和变哈达玛-伯格曼卷积算子的有界性

摘要本文继续研究复平面单位盘中的哈达玛-伯格曼算子。这些算子是正交投影的自然广义化，代表了乘法算子的积分实现。然而，研究积分形式的算子在应用积分算子理论以及研究某些函数空间（如全态荷尔德函数）方面具有许多优势，而乘法器理论并不适用于这些函数空间。作为主要结果，我们利用早先在实分析中发展起来的同质核算子技术，证明了哈达玛-伯格曼算子和变哈达玛-伯格曼算子的有界性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.