Affiliation:
1. Department of Mathematics , Indian Institute of Technology Hyderabad , Sangareddy , India
Abstract
Abstract
In the present article, we give an alternate and easier proof for the image characterization of
L
2
(
ℝ
2
n
)
{L^{2}(\mathbb{R}^{2n})}
under the twisted Bargmann transform which was earlier studied by Krontz, Thangavelu and Xu. As a consequence, we study some properties of the twisted Bergman spaces for
0
<
p
≤
∞
{0<p\leq\infty}
and the
L
p
{L^{p}}
-boundedness of the twisted Bargmann transform,
1
≤
p
≤
∞
{1\leq p\leq\infty}
. We also study
L
p
{L^{p}}
-boundedness of the twisted Bargmann projection
P
t
{P_{t}}
and the duality relations between the spaces
B
t
p
(
ℂ
2
n
)
{B_{t}^{p}(\mathbb{C}^{2n})}
,
1
<
p
<
∞
{1<p<\infty}
.
Subject
Applied Mathematics,General Mathematics
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