Displaying similar documents to “Bloch-to-Hardy composition operators”

Holomorphic Bloch spaces on the unit ball in C n

A. V. Harutyunyan, Wolfgang Lusky (2009)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

This work is an introduction to anisotropic spaces of holomorphic functions, which have ω -weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding L ω ∞ space. We establish a description of ( A p ( ω ) ) * via the Bloch classes for all 0 < p ≤ 1 .

ω –weighted holomorphic Besov spaces on the unit ball in C n

A. V. Harutyunyan, Wolfgang Lusky (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The ω -weighted Besov spaces of holomorphic functions on the unit ball B n in C n are introduced as follows. Given a function ω of regular variation and 0 < p < ∞ , a function f holomorphic in B n is said to belong to the Besov space B p ( ω ) if ∥ f ∥ B p ( ω ) p = ∫ B n ( 1 - | z | 2 ) p | D f ( z ) | p ω ( 1 - | z | ) ( 1 - | z | 2 ) n + 1 d ν ( z ) < + ∞ , where d ν ( z ) is the volume measure on B n and D stands for the fractional derivative of f . The holomorphic Besov space is described in the terms of the corresponding L p ( ω ) space. Some projection theorems and theorems on existence of the inversions of these projections are proved....