An optimal Sobolev embedding for L1

Daniel Spector*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Article number108559
JournalJournal of Functional Analysis
Issue number3
Publication statusPublished - 2020 Aug 15


  • L-type estimates
  • Riesz potentials
  • Sobolev embeddings

ASJC Scopus subject areas

  • Analysis


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