Directional maximal function along the primes

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Laura Cladek
UCLA. Department of Mathematics
https://orcid.org/0000-0002-7528-9238
José Madrid
UCLA. Department of Mathematics
Polona Durcik
California Institute of Technology
Ben Krause
Princeton University. Department of Mathematics

We study a two-dimensional discrete directional maximal operator along the set of the prime numbers. We show existence of a set of vectors, which are lattice points in a sufficiently large annulus, for which the ` 2 norm of the associated maximal
operator, with supremum taken over all large scales, grows with an epsilon power in the number of vectors. This paper is a follow-up to a prior work on the discrete directional maximal operator along the integers by the first and third author.

Paraules clau
maximal functions, Fourier transform, circle method

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Com citar
Cladek, Laura et al. “Directional maximal function along the primes”. Publicacions Matemàtiques, vol.VOL 65, no. 2, pp. 841-58, https://raco.cat/index.php/PublicacionsMatematiques/article/view/390254.
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