On weighted spaces of holomorphic functions of several variables |
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Authors: | Wolfgang Lusky Jari Taskinen |
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Institution: | 1.Instit?t für Mathematik,Universit?t Paderborn,Paderborn,Germany;2.Department of Mathematics and Statistics,University of Helsinki,Helsinki,Finland |
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Abstract: | We generalize the results of 11] and 12] for the unit ball $
\mathbb{B}_d
$
\mathbb{B}_d
of ℂ
d
. In particular, we show that under the weight condition (B) the weighted H
∞-space on $
\mathbb{B}_d
$
\mathbb{B}_d
is isomorphic to ℓ∞ and thus complemented in the corresponding weighted L
∞-space. We construct concrete, generalized Bergman projections accordingly. We also consider the case where the domain is
the entire space ℂ
d
. In addition, we show that for the polydisc $
\mathbb{D}^d
$
\mathbb{D}^d
d
, the weighted H
∞-space is never isomorphic to ℓ∞. |
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Keywords: | |
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