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.
|Number of pages||17|
|Journal||Bulletin of the London Mathematical Society|
|Publication status||Published - 2021 Jun|
- 26A46 (secondary)
- 42A45 (primary)
ASJC Scopus subject areas