On the convergence of products of operator nets

TL;DR

This paper generalizes a classical theorem to abstract measure spaces and discusses applications in harmonic analysis, providing new insights into the convergence behavior of operator nets.

Contribution

It extends the Jessen-Marcinkiewicz-Zygmund theorem to abstract spaces and reviews related harmonic analysis applications.

Findings

Generalized convergence results for operator nets.

Applications to classical harmonic analysis.

Enhanced understanding of operator product behavior.

Abstract

The generalization of the Jessen-Marcinkiewicz-Zygmund-type theorem for the abstract space with measure was obtained in current paper. Some applications to classical harmonic analysis were reviewed.