Sparse bounds for discrete maximal functions associated with Birch–Magyar averages

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 $$-estimates for such discrete maximal functions over sparse sequences for all $$. The proof of sparse bounds is based on scale-free $$-improving estimates for the single scale Birch–Magyar averages.