A note on discrete spherical averages over sparse sequences

DOI10.1090/proc/14575zbMath1497.42042arXiv1808.03822OpenAlexW2962676204WikidataQ114094226 ScholiaQ114094226MaRDI QIDQ5869405

Brian Cook

Publication date: 28 September 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.03822

zbMATH Keywords

normalized discrete spherical convolution

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Convolution, factorization for one variable harmonic analysis (42A85)

Related Items (1)

Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres

Cites Work

• Averages in the plane over convex curves and maximal operators
• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• Maximal and singular integral operators via Fourier transform estimates
• Discrete analogues in harmonic analysis: spherical averages
• \(\ell^p\)-improving inequalities for discrete spherical averages
• The discrete spherical averages over a family of sparse sequences
• Maximal function inequalities and a theorem of Birch
• Forms in many variables
• Maximal functions: Spherical means
• Diophantine equations and ergodic theorems

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