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arXiv · 1909.13319

Directional maximal function along the primes

Laura Cladek·Polona Durcik·Ben Krause·José Madrid
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Abstract

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 $\ell^2$ 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.

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Laura Cladek, Polona Durcik, Ben Krause, José Madrid. 2019-09-29. Directional maximal function along the primes. https://arxiv.org/abs/1909.13319

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