Distances from Bloch functions to some Möbius invariant function spaces in the unit ball of ℂn

Wen Xu

doi:10.1155/2009/942143

Abstract

Distance formulae from Bloch functions to some Möbius invariant function spaces in the unit ball of ℂnsuch asQsspaces, little Bloch spaceℬ0and Besov spacesBpare given.

Highlights

Let B be the unit ball of Cn with boundary S, let dν denote the Lebesgue measure on B such that ν(B) = 1 and let dσ be the rotation invariant positive normalized measure on S, i.e. σ(S) = 1
For α > −1, the weighted Lebesgue measure dνα is defined by dνα(z) = cα(1 − |z|2)αdν(z), where
The purpose of this paper is to drive distance formulae from Bloch functions to some Mobius invariant function spaces on the unit ball which generalize the results of [7]

Summary

Introduction

The Bloch space on B , denoted by B , is the class of all functions f ∈ H(B), which satisfy f 1 = sup(1 − |z|2)|Rf (z)| < ∞. The purpose of this paper is to drive distance formulae from Bloch functions to some Mobius invariant function spaces on the unit ball which generalize the results of [7]. Μ is an s-Carleson measure if and only if sup a∈B B

Objectives

Results

Conclusion