一致局部空间和经典Sobolev嵌入定理的改进

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2018-10-01 DOI:10.4310/ARKIV.2018.V56.N2.A13

P. Rabier

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引用次数: 1

摘要

证明了如果f是RN上一个N>1的分布，如果∂jf∈Lj，σj∩LN,1 uloc且1≤pj≤N，当pj=1或N时σj=1，则f是有界的，连续的，在无穷远处有一个有限的常数径向极限。这里，Lp，σ是经典洛伦兹空间，luloc是lloc大于Lp的“一致局部”子空间，σ当pN当pj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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Uniformly local spaces and refinements of the classical Sobolev embedding theorems

We prove that if f is a distribution on RN with N>1 and if ∂jf∈Lj ,σj ∩LN,1 uloc with 1≤pj≤N and σj=1 when pj=1 or N, then f is bounded, continuous and has a finite constant radial limit at infinity. Here, Lp,σ is the classical Lorentz space and L uloc is a “uniformly local” subspace of L loc larger than L p,σ when p<∞. We also show that f∈BUC if, in addition, ∂jf∈Lj ,σj ∩Lquloc with q>N whenever pj

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来源期刊

Arkiv for Matematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishing research papers, of short to moderate length, in all fields of mathematics.