Abstract. In this paper, we introduce the F (p, s)-Teichmüller space and investigate its Schwarzian derivative model and pre-logarithmic derivative model. In particular, we prove that the pre-logarithmic derivative model is a disconnected subset of Besov type space F (p, s) and the Bers projection is holomorphic.
IntroductionLet ∆ = {z : |z| < 1} be the unit disk in the complex plane C, ∆ * = C\∆ be the outside of the unit disk and S 1 = {z ∈ C : |z| = 1} be the unit circle. Let α > 0, the Bloch-type space B α consists of all holomorphic functions f on ∆ such thatand the subspace B α 0 consists of all functions f ∈ B α such thatWe denote by BMO(S 1 ) the space of all integrable functions on S 1 such thatwhere I is any arc on S 1 , |I| denotes the Lebesgue measure of I, andis the average of u over I. A holomorphic function f on ∆ belongs to BMOA(∆) if and only if it is a Poisson integral of some function which belongs to BMO(S 1 ). For any a ∈ ∆, set ϕ a (z) = z−a 1−az , z ∈ ∆. For p > 1, q > −2 and s ≥ 0, the space F (p, q, s) consists of all holomorphic functions f on the unit disk ∆ with the
Let Γ be a Fuchsian group. Any [μ] in the Teichmüller space T (Γ) determines a quasi-circle f μ (∂D). In this paper, we prove that, for any Fuchsian group Γ of the second kind, the Hausdorff dimension δ([μ]) = dimf μ (∂D) is not a real analytic function in T (Γ).
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