具有径向对称性的分数超和次谐函数的紧凑嵌入

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-18 DOI:10.1007/s00041-024-10082-2

Jacopo Bellazzini, Vladimir Georgiev

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引用次数: 0

摘要

我们证明了具有径向对称性的分数超和次谐函数在索波列夫空间中嵌入的紧凑性。主要工具是径向对称函数的点式衰减，该函数属于由有限同质索波列夫规范和有限 \(L^2\) Riesz 势规范定义的函数空间。作为副产品，我们还证明了径向对称分数超和次谐函数在索波列夫空间中插值不等式的最大化存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Compact Embeddings for Fractional Super and Sub Harmonic Functions with Radial Symmetry

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Compact Embeddings for Fractional Super and Sub Harmonic Functions with Radial Symmetry

We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by finite homogeneous Sobolev norm together with finite \(L^2\) norm of the Riesz potentials. As a byproduct we prove also existence of maximizers for the interpolation inequalities in Sobolev spaces for radially symmetric fractional super and sub harmonic functions.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.