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 |
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文章編號 | 108559 |
期刊 | Journal of Functional Analysis |
卷 | 279 |
發行號 | 3 |
DOIs | |
出版狀態 | 已發佈 - 2020 8月 15 |
ASJC Scopus subject areas
- 分析