赫兹型空间上里兹势的迹原理及其应用

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-09-03 DOI:10.1186/s13660-024-03192-4

M. Ashraf Bhat, G. Sankara Raju Kosuru

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引用次数: 0

摘要

我们为赫兹型空间上的里兹势建立了迹不等式，并研究了施加在特定参数上的条件的最优性。我们还以索波列夫型不等式的形式介绍了一些应用，包括赫兹空间环境下的加利亚多-尼伦堡-索波列夫不等式和分数积分定理。此外，我们还获得了赫兹型索波列夫空间的索波列夫嵌入定理。

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Trace principle for Riesz potentials on Herz-type spaces and applications

We establish trace inequalities for Riesz potentials on Herz-type spaces and examine the optimality of conditions imposed on specific parameters. We also present some applications in the form of Sobolev-type inequalities, including the Gagliardo–Nirenberg–Sobolev inequality and the fractional integration theorem in the Herz space setting. In addition, we obtain a Sobolev embedding theorem for Herz-type Sobolev spaces.

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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.