Sobolev regularity of the Beurling transform on planar domains

• Autores: Martí Prats Soler
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 61, Nº 2, 2017, págs. 291-336
• Idioma: inglés
• DOI: 10.5565/327583
• Enlaces
  • Texto completo  1    2  
• Resumen

  • Consider a Lipschitz domain Ω and the Beurling transform of its characteristic function BχΩ(z) = −p.v. 1 πz2 ∗ χΩ(z). It is shown that if the outward unit normal vector N of the boundary of the domain is in the trace space of Wn,p(Ω) (i.e., the Besov space Bn−1/p p,p (∂Ω)) then BχΩ ∈ Wn,p(Ω). Moreover, when p > 2 the boundedness of the Beurling transform on Wn,p(Ω) follows. This fact has farreaching consequences in the study of the regularity of quasiconformal solutions of the Beltrami equation.