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

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.