\ℓ^p(\ℤ^d)-Improving Properties and Sparse Bounds for\n Discrete Spherical Maximal Means, Revisited

2018/09/17 by Robert Kesler, Kesler, Robert
Mathematics · #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1809.06468

openalex publication_date 2018/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an expanded range of \ℓ ^p(\ℤ^d)-improving properties\nand sparse bounds for discrete spherical maximal means in every dimension\nd\≥ 6. Essential elements of the proofs are bounds for high exponent\naverages of Ramanujan and restricted Kloosterman sums.\n

Related

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