Beurling–Ahlfors extension by heat kernel, A-weights for VMO, and vanishing Carleson measures

Huaying Wei, Katsuhiko Matsuzaki

Research output: Contribution to journalArticlepeer-review


We investigate a variant of the Beurling–Ahlfors extension of quasisymmetric homeomorphisms of the real line that is given by the convolution of the heat kernel, and prove that the complex dilatation of such a quasiconformal extension of a strongly symmetric homeomorphism (that is, its derivative is an (Formula presented.) -weight whose logarithm is in VMO) induces a vanishing Carleson measure on the upper half-plane.

Original languageEnglish
JournalBulletin of the London Mathematical Society
Publication statusAccepted/In press - 2021


  • 26A46 (secondary)
  • 30C62
  • 30H35
  • 42A45 (primary)

ASJC Scopus subject areas

  • Mathematics(all)

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