Published July 1, 2021
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Directional maximal function along the primes
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.
Additional Information
© 2021 Departament de Matemàtiques, Universitat Autònoma de Barcelona. The authors are thankful for the comments of the anonymous referees.Attached Files
Published - PUBLMAT6522113.pdf
Submitted - 1909.13319.pdf
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Additional details
- Eprint ID
- 109754
- Resolver ID
- CaltechAUTHORS:20210707-223531817
- Created
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2021-07-08Created from EPrint's datestamp field
- Updated
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2021-07-08Created from EPrint's last_modified field