Distance from Bloch-Type Functions to the Analytic SpaceF(p,q,s)

Abstract

The analytic spaceF(p,q,s)can be embedded into a Bloch-type space. We establish a distance formula from Bloch-type functions toF(p,q,s), which generalizes the distance formula from Bloch functions to BMOA by Peter Jones, and toF(p,p-2,s)by Zhao.

On F(p, q, s) Spaces

“…The next result extends Jones' result to the distance formula from a function in B α to F (p, pα − 2, s). The result was first obtained by the author in [74] for the distance from B to F (p, p − 2, s), and then was extended for the distance from B α to F (p, q, s) with q = pα − 2 by Yuan and Tong in [64].…”

“…The proof follows the proof of Theorem 2 in [74]. The proof given in [64] uses a different method. Let f ∈ B α .…”

Distance Formulas on Weighted Banach Spaces of Analytic Functions

“…There are some other recent papers dealing with distance formulas. See [11] and the references therein.…”

An integral operator preserving s-Carleson measure on the unit ball

“…As the sequel of [10], this manuscript aims to characterize the distance from f ∈ B α to F (p, q, s) on B n as an application of Theorem 1. Let X ⊂ B α be an analytic function space.…”

“…The argument in our proof of Theorem 2 is a generalization of [10], which follows from Theorem 3.1.3 in [7]. The distance from a B α function to Campanato-Morrey space on D was given in [8] with the similar idea.…”