Sharp $L^p$-$L^q$ estimate fof the spectral projection associated with the twisted Laplacian

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2020-08-21 DOI:10.5565/publmat6622210

Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu

引用次数: 5

Abstract

In this note we are concerned with estimates for the spectral projection operator $\mathcal{P}_\mu$ associated with the twisted Laplacian $L$. We completely characterize the optimal bounds on the operator norm of $\mathcal{P}_\mu$ from $L^p$ to $L^q$ when $1\le p\le 2\le q\le \infty$. As an application, we obtain uniform resolvent estimate for $L$.

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与扭曲拉普拉斯算子相关的谱投影的夏普$L^p$-$L^q$估计

在这篇笔记中，我们关注与扭曲拉普拉斯$L$相关的谱投影算子$\mathcal{P}_\mu$的估计。在$1\le p\le 2\le q\le \infty$时，我们完整地刻画了$\mathcal{P}_\mu$从$L^p$到$L^q$的算子范数的最优界。作为应用，我们得到了$L$的均匀分辨率估计。

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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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.