Beurling-Ahlfors extension by heat kernel, ${\rm A}_\infty$-weights for VMO, and vanishing Carleson measures
Complex Variables
2021-01-27 v1 Analysis of PDEs
Abstract
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 (i.e. its derivative is an -weight whose logarithm is in VMO) induces a vanishing Carleson measure on the upper half-plane.
Keywords
Cite
@article{arxiv.2008.00897,
title = {Beurling-Ahlfors extension by heat kernel, ${\rm A}_\infty$-weights for VMO, and vanishing Carleson measures},
author = {Huaying Wei and Katsuhiko Matsuzaki},
journal= {arXiv preprint arXiv:2008.00897},
year = {2021}
}