Shannon, Sobolev and uncertainty inequalities for the Weinstein transform

IF 0.7 3区 数学 Q2 MATHEMATICS
N. B. Salem
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引用次数: 0

Abstract

ABSTRACT The objective of this paper is to extend some weighted inequalities for the Weinstein transform. Especially, we are interesting in the study of the Beckner logarithmic inequality, the Shannon inequality. We give a sharp version of this inequality. Next, we establish different Sobolev type embedding theorems in our context. Finally, we deal with some uncertainty inequalities and a logarithmic uncertainty inequality for the Weistein transform.
Shannon, Sobolev和Weinstein变换的不确定性不等式
摘要本文的目的是推广Weinstein变换的一些加权不等式。特别是,我们对Beckner对数不等式,Shannon不等式的研究很感兴趣。我们给出了这种不平等的一个尖锐的版本。接下来,我们在我们的上下文中建立了不同的Sobolev型嵌入定理。最后,我们讨论了Weistein变换的一些不确定性不等式和一个对数不确定性不等式。
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
CiteScore
2.20
自引率
20.00%
发文量
49
审稿时长
6-12 weeks
期刊介绍: Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.
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