沿素数方向的极大函数

Pub Date : 2019-09-29 DOI:10.5565/PUBLMAT6522113

Laura Cladek, Polona Durcik, B. Krause, Jos'e Madrid

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引用次数: 0

摘要

我们研究了一个沿素数集的二维离散方向极大算子。我们证明了一组向量的存在性，这些向量是足够大的环中的格点，对于这些向量，具有上确界的相关极大算子的$\ell^2$范数随着向量数量的ε幂而增长。本文是第一作者和第三作者先前关于沿整数的离散方向极大算子的工作的后续。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Directional maximal function along the primes

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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