Weighted inequlities for a generalized dyadic maximal operator involving the infinite product

TL;DR

This paper introduces a generalized dyadic maximal operator involving infinite products, establishing weighted inequalities and a Carleson embedding theorem, with results based on a generalized Hölder's inequality.

Contribution

It presents a novel generalized dyadic maximal operator involving infinite products and proves weighted inequalities and a Carleson embedding theorem for it.

Findings

Weighted inequalities for the generalized operator established

A formulation of the Carleson embedding theorem proved

Results rely on a generalized Hölder's inequality

Abstract

We define a generalized dyadic maximal operator involving the infinite product and discuss weighted inequalities for the operator. A formulation of the Carleson embedding theorem is proved. Our results depend heavily on a generalized H\"{o}lder's inequalities.