Directional maximal function along the primes

  title={Directional maximal function along the primes},
  author={Laura Cladek and Polona Durcik and Ben Krause and Jos'e Madrid},
  journal={Publicacions Matem{\`a}tiques},
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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