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Boundedness criterion for integral operators on the fractional Fock–Sobolev spaces
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Boundedness criterion for integral operators on the fractional Fock–Sobolev spaces
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Journal Article
Boundedness criterion for integral operators on the fractional Fock–Sobolev spaces
2022
Overview
We provide a boundedness criterion for the integral operator
S
φ
on the fractional Fock–Sobolev space
F
s
,
2
(
C
n
)
,
s
≥
0
, where
S
φ
(introduced by Zhu [
18
]) is given by
S
φ
F
(
z
)
:
=
∫
C
n
F
(
w
)
e
z
·
w
¯
φ
(
z
-
w
¯
)
d
λ
(
w
)
with
φ
in the Fock space
F
2
(
C
n
)
and
d
λ
(
w
)
:
=
π
-
n
e
-
|
w
|
2
d
w
the Gaussian measure on the complex space
C
n
. This extends the recent result in Cao et al. (Adv Math 363: 107001, 33 pp, 2020). The main approach is to develop multipliers on the fractional Hermite–Sobolev space
W
H
s
,
2
(
R
n
)
.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
