Norms of inclusions between some spaces of analytic functions

The inclusions between the Besov spaces $$B^q$$ B q , the Bloch space $$\mathcal {B}$$ B and the standard weighted Bergman spaces $$A^p_{\alpha}$$ A α p are completely understood, but the norms of the corresponding inclusion operators are in general unknown. In this work, we compute or estimate asymptotically the norms of these inclusions.

A criterion for normality of analytic mappings

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

Integral Superposition-Type Operators on Some Analytic Function Spaces

All entire functions which transform a class of holomorphic Zygmund-type spaces into weighted analytic Bloch space using the so-called n -generalized superposition operator are characterized in this paper. Moreover, certain specific properties such as boundedness and compactness of the newly defined class of generalized integral superposition operators are discussed and established by using the concerned entire functions.

Multipliers and closures of Besov-type spaces in the Bloch space

Let p > 1 and let ? be a non-negative function defined in R+. A function f ? H(D) belongs to the space Bp(?) (see [4]) if ||f||p Bp(?) = |f(0)jp + ?D |(1-|z|2) f?(z)|p ?(1-|z|2)/(1-|z|2)2 dA(z) < ?. In this paper, motivated by the works of B?koll? and Bao and G???s, under some conditions on the weight function ?, we investigate the closures CB(B ? Bp(?)) of the spaces B ? Bp(?) in the Bloch space. Moreover we prove that interpolating Blaschke products in CB(B ? Bp(?)) are multipliers of Bp(?) ? BMOA.