Directional maximal function along the primes

DOI10.5565/PUBLMAT6522113zbMath1480.42025arXiv1909.13319OpenAlexW3176057413MaRDI QIDQ2232025

Polona Durcik, Ben Krause, Laura Cladek, J. A. Jiménez Madrid

Publication date: 1 October 2021

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.13319

zbMATH Keywords

Fourier transformcircle methodmaximal functions

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Applications of the Hardy-Littlewood method (11P55) Discrete version of topics in analysis (39A12)

Cites Work

• Pointwise ergodic theorem along the prime numbers
• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• Maximal functions associated to rectangles with uniformly distributed directions
• Maximal operators over arbitrary sets of directions
• L ² bounds for a Kakeya-type maximal operator in ℝ³
• Singular integrals along 𝑁 directions in ℝ²
• Variational estimates for averages and truncated singular integrals along the prime numbers
• Some connections between Falconer's distance set conjecture and sets of Furstenburg type

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