广义Orlicz-Sobolev空间中的插值不等式及其应用

IF 0.9 4区数学 Q1 MATHEMATICS

Open Mathematics Pub Date : 2023-01-01 DOI:10.1515/math-2022-0595

Rui Wu, Songbai Wang

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引用次数: 0

摘要

摘要设m∈Nm\在｛\mathbb｛N｝｝中，是一个广义Orlicz函数。我们得到了广义Orlicz-Sobolev空间Wm，φ（Rn）｛W｝^｛m，\varphi｝\left（｛\mathbb｛R｝｝}^｛n｝）中导数的一些插值不等式。作为应用，我们在广义Orlicz空间中建立了域上的紧致Sobolev嵌入和Landau-Kolmogorov型不等式。介绍了Sobolevφ\varphi-容量，并研究了它的一些性质。

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Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications

Abstract Let m ∈ N m\in {\mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces W m , φ ( R n ) {W}^{m,\varphi }\left({{\mathbb{R}}}^{n}) . As applications, we established a compact Sobolev embedding on domain and a Landau-Kolmogorov-type inequality in generalized Orlicz spaces. And we introduced the Sobolev φ \varphi -capacity and studied some of its properties.

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来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: