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

Huaying Wei; Katsuhiko Matsuzaki

doi:10.1112/blms.12454

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

Huaying Wei, Katsuhiko Matsuzaki

School of Education

Research output: Contribution to journal › Article › peer-review

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 (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 language	English
Journal	Bulletin of the London Mathematical Society
DOIs	https://doi.org/10.1112/blms.12454
Publication status	Accepted/In press - 2021

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1112/blms.12454

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

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 (that is, its derivative is an (Formula presented.) -weight whose logarithm is in VMO) induces a vanishing Carleson measure on the upper half-plane.",

keywords = "26A46 (secondary), 30C62, 30H35, 42A45 (primary)",

author = "Huaying Wei and Katsuhiko Matsuzaki",

note = "Funding Information: This research is supported by the National Natural Science Foundation of China (Grant No. 11501259) and Japan Society for the Promotion of Science (KAKENHI 18H01125). ",

year = "2021",

doi = "10.1112/blms.12454",

language = "English",

journal = "Bulletin of the London Mathematical Society",

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T1 - Beurling–Ahlfors extension by heat kernel, A∞-weights for VMO, and vanishing Carleson measures

AU - Wei, Huaying

AU - Matsuzaki, Katsuhiko

N1 - Funding Information: This research is supported by the National Natural Science Foundation of China (Grant No. 11501259) and Japan Society for the Promotion of Science (KAKENHI 18H01125).

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - 26A46 (secondary)

KW - 30C62

KW - 30H35

KW - 42A45 (primary)

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