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Directional maximal function along the primes

Cladek, Laura and Durcik, Polona and Krause, Ben and Madrid, José (2021) Directional maximal function along the primes. Publicacions Matemàtiques, 65 (2). pp. 841-858. ISSN 0214-1493. doi:10.5565/publmat6522113.

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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 ℓ² 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.

Item Type:Article
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Additional Information:© 2021 Departament de Matemàtiques, Universitat Autònoma de Barcelona. The authors are thankful for the comments of the anonymous referees.
Subject Keywords:maximal functions, Fourier transform, circle method
Issue or Number:2
Classification Code:2010 Mathematics Subject Classification: 42B25, 11P55, 39A12
Record Number:CaltechAUTHORS:20210707-223531817
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109754
Deposited By: Tony Diaz
Deposited On:08 Jul 2021 16:57
Last Modified:08 Jul 2021 16:57

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