Fractional integration and optimal estimates for elliptic systems

Felipe Hernandez, Daniel Spector*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we give an affirmative answer to the Euclidean analogue of a question of Bourgain and Brezis concerning the optimal Lorentz estimate for a Div–Curl system: If F∈L1(R3;R3) satisfies divF=0 in the sense of distributions, then the function Z=curl(-Δ)-1F satisfies (Formula presented.) and there exists a constant C>0 such that (Formula presented.) Our proof relies on a new endpoint Hardy–Littlewood–Sobolev inequality for divergence free measures which we obtain via a result of independent interest, an atomic decomposition of such objects.

Original languageEnglish
Article number117
JournalCalculus of Variations and Partial Differential Equations
Issue number5
Publication statusPublished - 2024 Jun


  • 31B10
  • 35J46
  • 46E35

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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