The $p$-integrable Teichmüller space for $p⩾1$

Abstract

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

Modifications to the published article are made on this follow-up version. (Lemma 3.2 and Theorem 4.1 are improved.)

References in corpus (2)

• The $p$-Weil-Petersson Teichmüller space and the quasiconformal extension of curves
• Beurling-Ahlfors extension by heat kernel, ${\mathrm{A}}_{\infty }$-weights for VMO, and vanishing Carleson measures

Cited by in corpus (1)

• The complex structure of the Teichmüller space of circle diffeomorphisms in the Zygmund smooth class