Note on some asymptotic relations for Bloch functions and the distance from a Bloch function to the little Bloch space

Abstract

We prove, among other results, that if f is an analytic function on the open unit disc in the complex plane belonging to the Bloch space B, then the asymptotic relation holds dist(Formula presented) for each l ∈ N, where dist(Formula presented) and B<inf>0</inf> is the little Bloch space, extending a result in the literature concerning the case l = 1. In passing, we also obtain the following asymptotic relation dist(Formula presented).