A T(1) Theorem for Fractional Sobolev Spaces on Domains

Martí Prats, Eero Saksman

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)


© 2017, Mathematica Josephina, Inc. Given any uniform domain Ω , the Triebel–Lizorkin space Fp,qs(Ω) with 0 < s< 1 and 1 < p, q< ∞ can be equipped with a norm in terms of first-order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this new characterization, we prove a T(1)-theorem for fractional Sobolev spaces with 0 < s< 1 for any uniform domain and for a large family of Calderón–Zygmund operators in any ambient space Rd as long as sp> d.
Original languageEnglish
Pages (from-to)2490-2538
JournalJournal of Geometric Analysis
Issue number3
Publication statusPublished - 1 Jul 2017


  • Besov
  • Calderón–Zygmund operators
  • First-order differences
  • Fourier multipliers
  • Sobolev
  • Triebel–Lizorkin


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