Hardy Spaces of Certain Convolution Operator

TL;DR

This paper establishes conditions under which a generalized convolution operator belongs to Hardy spaces and bounded analytic functions, providing new theoretical insights and practical examples.

Contribution

It introduces novel conditions for convolution operators to be in Hardy spaces and bounded analytic functions, expanding the understanding of these operators.

Findings

Derived new criteria for convolution operators in Hardy spaces

Identified conditions ensuring boundedness of operators

Provided illustrative examples demonstrating the results

Abstract

In this article, we determine conditions on the parameters of a generalized convolution operator such that it belongs to the Hardy space and to the space of bounded analytic functions. Results obtained are new and their usefulness is depicted by deducing several interesting examples.