Directional maximal function along the primes

• Cladek, Laura ^[3] ; Madrid, José ^[3] ; Durcik, Polona ^[1] ; Krause, Ben ^[2]
  1. [1] California Institute of Technology

     California Institute of Technology

     Estados Unidos

     
  2. [2] Princeton University

     Princeton University

     Estados Unidos

     
  3. [3] UCLA. Department of Mathematics

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• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 2, 2021, págs. 841-858
• Idioma: inglés
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• Resumen

  • 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.