海森堡群上的对数索波列夫不等式及其在不确定性不等式和热方程中的应用

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-07-25 DOI:10.1186/s13660-024-03174-6

Takeshi Suguro

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引用次数: 0

摘要

我们考虑海森堡群上的对数索波列夫不等式。我们可以从索博列夫不等式推导出对数索博列夫不等式，并考虑将其应用于海森堡群上的不确定性不等式。此外，我们还可以从对数索波列夫不等式得到海森堡群上热方程解的耗散估计。

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The logarithmic Sobolev inequality on the Heisenberg group and applications to the uncertainty inequality and heat equation

We consider the logarithmic Sobolev inequality on the Heisenberg group. One can derive the logarithmic Sobolev inequality from the Sobolev inequality, and we consider an application to the uncertainty inequality on the Heisenberg group. Moreover, one can also obtain a dissipative estimate of a solution of the heat equation on the Heisenberg group from the logarithmic Sobolev inequality.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.