广义傅立叶型变换的加权范数不等式及其应用

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2018-12-05 DOI:10.5565/publmat6412001

A. Debernardi

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引用次数: 7

摘要

得到了广义傅里叶变换在有权的L^p-L^q$空间之间有界的权值的充要条件。作为一个重要的例子，我们研究了幂型核的变换，例如sin, Hankel或$\mathscr{H}_\alpha$变换。所得到的充分必要条件是用权的形式给出的，而不是用它们的递减重排的形式给出的，这与前面的几个研究不同。

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Weighted norm inequalities for generalized Fourier-type transforms and applications

We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted $L^p-L^q$ spaces. As an important example, we investigate transforms with kernel of power type, as for instance the sine, Hankel or $\mathscr{H}_\alpha$ transforms. The obtained necessary and sufficient conditions are given in terms of weights, but not in terms of their decreasing rearrangements, as in several previous investigations.

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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.