
 
Integral Operators Between Fock Spaces∗ 
 
Citation： 
Yongqing LIU,Shengzhao HOU.Integral Operators Between Fock Spaces∗[J].Chinese Annals of Mathematics B,2024,45(2):265~278 
Page view： 698
Net amount： 280 
Authors： 
Yongqing LIU; Shengzhao HOU 
Foundation： 
This work was supported by the National Natural Science Foundation of China (No. 11971340). 


Abstract： 
In this paper, the authors study the integral operator
Sφf(z) = Z
C
φ(z, w)f(w)dλα(w)
induced by a kernel function φ(z, ·) ∈ F
∞α between Fock spaces. For 1 ≤ p ≤ ∞, they
prove that Sφ : F
1
α → F
p
α is bounded if and only if
sup
a∈C
kSφkakp,α < ∞, (?)
where ka is the normalized reproducing kernel of F
2
α; and, Sφ : F
1
α → F
p
α is compact if and
only if
lim
a→∞
kSφkakp,α = 0.
When 1 < q ≤ ∞, it is also proved that the condition (?) is not sufficient for boundedness
of Sφ : F
q
α → F
p
α .
In the particular case φ(z, w) = eαzw?(z ? w) with ? ∈ F
2
α, for 1 ≤ q < p < ∞, they
show that Sφ : F
p
α → F
q
α is bounded if and only if ? = 0; for 1 < p ≤ q < ∞, they give
sufficient conditions for the boundedness or compactness of the operator Sφ : F
p
α → F
q
α. 
Keywords： 
Fock spaces, Integral operators, Normalized reproducing kernel 
Classification： 
32A36, 45P05 

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