Sparse Bounds for Discrete Maximal Functions associated with Birch-Magyar averages

2024/12/09 by Ankit Bhojak, Bhojak, Ankit, Surjeet Singh Choudhary +4
Mathematics · #Limits and Structures in Graph Theory #Advanced Harmonic Analysis Research #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2412.06348

Abstract

In this article, we study discrete maximal function associated with the Birch-Magyar averages over sparse sequences. We establish sparse domination principle for such operators. As a consequence, we obtain ℓ^p-estimates for such discrete maximal function over sparse sequences for all p>1. The proof of sparse bounds is based on scale-free ℓ^p-improving estimates for the single scale Birch-Magyar averages.

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