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arXiv · 2412.06348

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

Ankit Bhojak·Surjeet Singh Choudhary·Siddhartha Samanta·Saurabh Shrivastava
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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 $\ell^p$-estimates for such discrete maximal function over sparse sequences for all $p>1$. The proof of sparse bounds is based on scale-free $\ell^p-$improving estimates for the single scale Birch-Magyar averages.

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Ankit Bhojak, Surjeet Singh Choudhary, Siddhartha Samanta, Saurabh Shrivastava. 2024-12-09. Sparse Bounds for Discrete Maximal Functions associated with Birch-Magyar averages. https://arxiv.org/abs/2412.06348

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