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

A. V. Harutyunyan, Wolfgang Lusky (2011)

Commentationes Mathematicae Universitatis Carolinae

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. Also,...

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