This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast εY -periodic conductivity. When the conductivity is bounded in L1 and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ε−2, the first Bloch eigenvalue converges as ε → 0 to a limit which preserves the second-order expansion w...

We give a criterion for q-valent analytic functions in the unit disk to belong to Q K , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nonde-creasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Q p spaces are obtained. 1. Introduction....

In this paper we characterize continuity and compactness of composition operators Cφ mapping the α-Bloch space into the μ-Bloch space, where μ is a weight defined on the unit disk D, in term of certain expression that involve the n-power of the symbol φ.