Open Access
June 2023 The $p$-integrable Teichmüller space for $p \geqslant 1$
Huaying Wei, Katsuhiko Matsuzaki
Proc. Japan Acad. Ser. A Math. Sci. 99(6): 37-42 (June 2023). DOI: 10.3792/pjaa.99.008


We verify that the $p$-integrable Teichmüller space $T_{p}$ admits the canonical complex Banach manifold structure for any $p \geq 1$. Moreover, we characterize a quasisymmetric homeomorphism corresponding to an element of $T_{p}$ in terms of the $p$-Besov space for any $p>1$.


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Huaying Wei. Katsuhiko Matsuzaki. "The $p$-integrable Teichmüller space for $p \geqslant 1$." Proc. Japan Acad. Ser. A Math. Sci. 99 (6) 37 - 42, June 2023.


Published: June 2023
First available in Project Euclid: 6 June 2023

MathSciNet: MR4602729
Digital Object Identifier: 10.3792/pjaa.99.008

Primary: 30C62 , 30H25 , 32G15
Secondary: 42A45 , 46G20

Keywords: analytic Besov space , Bers embedding , bi-Lipschitz quasiconformal extension , universal Teichmüller space , Weil–Petersson Teichmüller space

Rights: Copyright © 2023 The Japan Academy

Vol.99 • No. 6 • June 2023
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