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.

Bloch and Okounkov’s correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of ĝl ∞ modules of level one. Recent works have calculated these character functions for higher levels for ĝl ∞ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type D of h...

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...

Bloch and Okounkov’s correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of ĝl ∞ modules of level one. Recent works have calculated these character functions for higher levels for ĝl ∞ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type D of h...

and Applied Analysis 3 The weighted-type space H∞ μ B H ∞ μ 2, 3 consists of all f ∈ H B such that ‖f‖H∞ μ : sup z∈B μ z ∣ ∣f z ∣ ∣ < ∞, 1.11 where μ is a positive continuous function on B weight . The Bloch-type space Bμ B Bμ consists of all f ∈ H B such that ‖f‖Bμ : ∣ ∣f 0 ∣ ∣ sup z∈B μ z ∣ ∣Rf z ∣ ∣ < ∞, 1.12 where μ is a weight. Let g ∈ H D , g 0 0, and φ be a holomorphic self-map of B, the...

Abstract In this paper, we give a generalization and improvement of the Pavlović result on characterization continuously differentiable functions in Bloch space unit ball $\mathbb {R}^{m}$ . Then, derive Holland–Walsh type theorem for analytic normal mappings disk.

In this paper, the boundedness and compactness of weighted composition operators from analytic Morrey spaces into Bloch-type spaces and little Bloch-type spaces are studied.