Sharp $l^p$-improving estimates for the discrete paraboloid

TL;DR

This paper establishes optimal $l^p$-improving bounds for the averaging operator on the discrete paraboloid across all dimensions, advancing understanding of discrete harmonic analysis.

Contribution

It provides the first sharp $l^p$-improving estimates for the discrete paraboloid in all dimensions, filling a key gap in discrete harmonic analysis.

Findings

Proved sharp $l^p$-improving bounds for the discrete paraboloid

Established results in all dimensions $n \\ge 2$

Enhanced understanding of discrete harmonic analysis techniques

Abstract

We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\ge 2$.