Bootstrap methods in bounding discrete Radon operators

TL;DR

This paper develops bootstrap techniques to prove inequalities related to discrete Radon operators, enhancing understanding of their behavior in $ ext{ell}^p( ext{Z}^d)$ spaces.

Contribution

It introduces bootstrap methods to establish key inequalities for discrete Radon operators, a novel approach in this context.

Findings

Proved maximal inequalities for discrete Radon operators.

Established oscillation and variational inequalities.

Demonstrated jump inequalities for these operators.

Abstract

The aim of this paper is to develop bootstrap arguments to establish maximal, oscillation, variational and jump inequalities for the discrete averaging Radon operators on $\ell^p(\mathbb Z^d)$.