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arXiv · 2001.11557

New bounds for discrete lacunary spherical averages

Theresa C. Anderson·Jose Madrid
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Abstract

We show that the discrete lacunary spherical maximal function is bounded on $l^p(\mathbb{Z}^d)$ for all $p >\frac{d+1}{d-1}$. Our range is new in dimension 4, where it appears that little was previously known for general lacunary radii. Our technique follows that of Kesler-Lacey-Mena, using the Kloosterman refinement to improve the estimates in several places, which leads to an overall improvement in dimension 4.

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Theresa C. Anderson, Jose Madrid. 2020-01-30. New bounds for discrete lacunary spherical averages. https://arxiv.org/abs/2001.11557

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