沿素数方向的极大函数

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques 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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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.