Discrete multilinear spherical averages

TL;DR

This paper characterizes the boundedness of multilinear spherical maximal operators on integer lattice spaces, extending understanding of harmonic analysis in discrete settings.

Contribution

It provides a complete characterization of the boundedness conditions for multilinear spherical averages on discrete lattice spaces.

Findings

Established boundedness criteria for multilinear spherical maximal operators.

Extended harmonic analysis results to discrete integer lattice settings.

Identified key conditions for operator boundedness in pq spaces.

Abstract

In this note we give a characterization of $\ell^{p}\times ...\times \ell^{p}\to\ell^q$ boundedness of maximal operators associated to multilinear convolution averages over spheres in $\mathbb{Z}^n$.