An α-number characterization of Lp spaces on uniformly rectifiable sets

• Azzam, Jonas ^[1] ; Dąbrowski, Damian ^[2]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
  2. [2] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 67, Nº 0, 2023, págs. 819-850
• Idioma: inglés
• DOI: 10.5565/publmat6722313
• Enlaces
  • Texto completo
• Resumen

  • We give a characterization of Lp(σ) for uniformly rectifiable measures σ using Tolsa’s α-numbers, by showing, for 1 < p < ∞ and f ∈ Lp(σ), that kfkLp(σ) ∼Z ∞0(αfσ(x, r) + |f|x,rασ(x, r))2drr12Lp(σ).

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