J. Aust. Math. Soc.
74 (2003), 517

A characterization of weighted BergmanOrlicz spaces on the unit ball in

Yasuo Matsugu
Department of Mathematical Sciences
Faculty of Science
Shinshu University
3908621 Matsumoto
Japan
matsugu@math.shinshuu.ac.jp



Jun Miyazawa
Department of Mathematical Sciences
Faculty of Science
Shinshu University
3908621 Matsumoto
Japan



Abstract

Let
denote the unit ball in
, and
the normalized Lebesgue measure on
. For
, define
,
. Here
is a positive constant such
that . Let
denote the space of all holomorphic functions
in . For a twice differentiable, nondecreasing,
nonnegative strongly convex function
on the real line
, define the BergmanOrlicz space
by


In this paper we prove that a function
is in
if and only if


where
is the radial derivative of
.

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