Maximal Operators of Walsh-N\"orlund means On the Dyadic Hardy Spaces

TL;DR

This paper establishes necessary and sufficient conditions for the boundedness of maximal Walsh-Nörlund means operators with non-increasing weights from dyadic Hardy spaces to Lebesgue spaces.

Contribution

It provides a complete characterization of the boundedness criteria for Walsh-Nörlund maximal operators on dyadic Hardy spaces.

Findings

Boundedness characterized by specific weight conditions

Necessary and sufficient conditions derived

Extension of classical results to Walsh-Nörlund means

Abstract

The presented paper will be proved the necessary and sufficient conditions in order maximal operator of Walsh-N\"orlund means with non-increasing weights to be bounded from the dyadic Hardy space $H_{p}(\mathbb{I})$\ to the space $% L_{p}(\mathbb{I})$.