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arXiv · 2008.00897

Beurling-Ahlfors extension by heat kernel, ${\rm A}_\infty$-weights for VMO, and vanishing Carleson measures

Huaying Wei·Katsuhiko Matsuzaki
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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 ${\rm A}_\infty$-weight whose logarithm is in VMO) induces a vanishing Carleson measure on the upper half-plane.

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Huaying Wei, Katsuhiko Matsuzaki. 2020-08-03. Beurling-Ahlfors extension by heat kernel, ${\rm A}_\infty$-weights for VMO, and vanishing Carleson measures. https://doi.org/10.1112/blms.12454

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