New bounds for discrete lacunary spherical averages

2020/01/30 by Anderson, Theresa C., Madrid, Jose
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.11557

Abstract

We show that the discrete lacunary spherical maximal function is bounded on l^p(ℤ^d) for all p >(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.

Related

• Lacunary Discrete Spherical Maximal Functions
• Restricted weak-type endpoint estimates for discrete k-spherical maximal functions
• The discrete spherical averages over a family of sparse sequences
• Lebesgue bounds for multilinear spherical and lacunary maximal averages
• ℓ^p(ℤ^d)-Improving Properties and Sparse Bounds for Discrete Spherical Maximal Averages