A+ CATEGORY SCIENTIFIC UNIT

Heating of the Beurling operator: Sufficient conditions for the two-weight case

Volume 186 / 2008

S. Petermichl, J. Wittwer Studia Mathematica 186 (2008), 203-217 MSC: Primary 30Exx. DOI: 10.4064/sm186-3-1

Abstract

We establish sufficient conditions on the two weights $w$ and $v$ so that the Beurling–Ahlfors transform acts continuously from $L^2(w^{-1})$ to $L^2(v)$. Our conditions are simple estimates involving heat extensions and Green's potentials of the weights.

Authors

  • S. PetermichlDépartement de Mathématiques
    Université de Bordeaux 1
    351, Cours de la Libération
    33405 Talence, France
    e-mail
  • J. WittwerWestminster College
    1840 S 1300 E
    Salt Lake City, UT 84105, U.S.A.
    e-mail

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