Resumen de Directional maximal function along the primes

Laura Cladek, José Ramón Madrid Padilla, Polona Durcik, Ben Krause

• 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 maximaloperator, 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.