# Variants of the Inequalities of Paley and Zygmund

## TL;DR

This paper explores extensions of the classical Paley and Zygmund inequalities to multivariable functions, providing sharp multiplier inclusion theorems and variants on the real line.

## Contribution

It introduces new multivariable versions of Paley and Zygmund inequalities and establishes sharp multiplier inclusion theorems.

## Key findings

- New multivariable inequalities derived
- Sharp multiplier inclusion theorems proved
- Variants on the real line developed

## Abstract

We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.