J. Aust. Math. Soc.
74 (2003), 5-17
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A characterization of weighted Bergman-Orlicz spaces on the unit ball in
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Yasuo Matsugu
Department of Mathematical Sciences
Faculty of Science
Shinshu University
390-8621 Matsumoto
Japan
matsugu@math.shinshu-u.ac.jp
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Jun Miyazawa
Department of Mathematical Sciences
Faculty of Science
Shinshu University
390-8621 Matsumoto
Japan
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Abstract
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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 Bergman-Orlicz space
by
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In this paper we prove that a function
is in
if and only if
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where
is the radial derivative of
.
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