On the regularity of generic Hausdorff-type transformations

TL;DR

This paper introduces a generalized class of Hausdorff-type operators with variable-dependent kernels and extends classical regularity results to these operators, broadening the understanding of summation method behaviors.

Contribution

It defines a new class of Hausdorff-type operators with variable-dependent kernels and proves their regularity properties, generalizing classical summation method results.

Findings

Established regularity conditions for the new class of operators

Extended classical summation method results to variable-dependent kernels

Provided a framework for analyzing generalized Hausdorff-type transformations

Abstract

The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity of various summation methods are proved for the case of such operators.