Hardy-Littlewood inequalities for multipolynomials

TL;DR

This paper extends the Hardy-Littlewood inequalities to multipolynomials, a recent mathematical concept, and introduces a related variant of the Kahane-Salem-Zygmund inequality within this framework.

Contribution

It proves Hardy-Littlewood inequalities for multipolynomials and presents a new variant of the Kahane-Salem-Zygmund inequality for this class.

Findings

Hardy-Littlewood inequalities established for multipolynomials

A variant of the Kahane-Salem-Zygmund inequality developed for multipolynomials

Advances the theory of multipolynomials by connecting it with classical inequalities.

Abstract

The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving Hardy- Littlewood inequalities for multipolynomials and, en passant, a variant of the Kahane- Salem-Zygmund inequality in this framework.