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

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED Journal of Fourier Analysis and Applications Pub Date : 2024-04-18 DOI:10.1007/s00041-024-10082-2

Jacopo Bellazzini, Vladimir Georgiev

引用次数: 0

Abstract

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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具有径向对称性的分数超和次谐函数的紧凑嵌入

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。

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来源期刊

Journal of Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications

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