Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 705-712

FUNCTIONS IN BLOCH-TYPE SPACES AND THEIR MODULI

Konstantin M. Dyakonov

ICREA, BGSMath and Universitat de Barcelona, Departament de Matemàtiques i Informàtica
Gran Via 585, E-08007 Barcelona, Spain; konstantin.dyakonov 'at' icrea.cat

Abstract. Given a suitably regular nonnegative function ω on (0,1], let B_ω denote the space of all holomorphic functions f on the unit ball B_n of Cⁿ that satisfy

|∇f(z)| ≤ C ω(1-|z|)/(1-|z|), z ∈ B_n,

with some fixed C = C_f > 0. We obtain a new characterization of B_ω functions in terms of their moduli.

2010 Mathematics Subject Classification: Primary 30H05, 32A37, 32A38, 46J10.

Key words: Holomorphic functions, Bloch-type spaces, Lipschitz spaces.

Reference to this article: K.M. Dyakonov: Functions in Bloch-type spaces and their moduli. Ann. Acad. Sci. Fenn. Math. 41 (2016), 705-712.

Full document as PDF file

doi:10.5186/aasfm.2016.4143