An analytic function φ mapping the unit disk into itself is said to belong to the hyperbolic little Bloch class if the ratio (1−|z|2)|φ′(z)|/(1−|φ(z)|2) converges to 0 as |z| → 1, while φ is in the little Bloch space if just the numerator of this expression converges to zero. Several constructions of inner functions in the little Bloch space have recently appeared. In this paper we construct a ...

We introduce a class of Möbius invariant spaces of analytic functions in the unit disk, characterize these spaces in terms of Carleson type measures, and obtain a necessary and sufficient condition for a lacunary series to be in such a space. Special cases of this class include the Bloch space, the diagonal Besov spaces, BMOA, and the so-called Qp spaces that have attracted much attention lately.

The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

Let φ and ψ be holomorphic maps on such that φ( ) ⊂ . Let Cφ,Mψ and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces AβN to Bloch-type spaces. In fact, we prove that these operators map AβN compactly into Bloch-type spaces if and only if they map A β...

We discuss a method for determining the optimally localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ‘‘generalized Wannier functions’’ we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread (n^r &n2^r&n 2 of the Wann...