New bounds for discrete lacunary spherical averages
Abstract
We show that the discrete lacunary spherical maximal function is bounded on lp(Zd) for all p >d+1d-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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