An optimal Sobolev embedding for L1

Daniel Spector*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

4 引文 斯高帕斯(Scopus)

摘要

In this paper we establish an optimal Lorentz space estimate for the Riesz potential acting on curl-free vectors: There is a constant C=C(α,d)>0 such that ‖IαF‖Ld/(d−α),1(Rd;Rd)≤C‖F‖L1(Rd;Rd) for all fields F∈L1(Rd;Rd) such that curlF=0 in the sense of distributions. This is the best possible estimate on this scale of spaces and completes the picture in the regime p=1 of the well-established results for p>1.

原文英語
文章編號108559
期刊Journal of Functional Analysis
279
發行號3
DOIs
出版狀態已發佈 - 2020 八月 15

ASJC Scopus subject areas

  • 分析

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