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. https://resolver.caltech.edu/CaltechAUTHORS:20210707-223531817
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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 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 | |||||||||
| DOI: | 10.5565/publmat6522113 | |||||||||
| Record Number: | CaltechAUTHORS:20210707-223531817 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210707-223531817 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 109754 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 08 Jul 2021 16:57 | |||||||||
| Last Modified: | 08 Jul 2021 16:57 |
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