Eddy Kwessi
CIMPA 2011-Buea University
Title: Characterization of Lacunary Functions
in Weighted Bergman-Besov-Lipschitz Spaces
Abstract
ρ
We consider the weighted-Bergman-Besov-Lipschitz
Z 1 Z 2πspace B of analytic
ρ(1 − r)
|F 0 (reiθ )|
functions F in the unit disc for which ||F ||B ρ =
dr
1−r
0
0
∞
X
and we show that a lacunary funtion F (z) =
an z n belongs to B ρ if and
n=1
only if sequence an satisfies
∞
X
!1/2
2n K(n, ρ)
n=1
X
|ak |2
< ∞, where In are
k∈In
some diadic intervals, ρ belongs to a certain class of weights and K(n, ρ) > 0
is a function of n and ρ.
1