Abstract
In this paper,the authors study the integral operator S φf(z)=∫cφ(z,(ω))f(ω)dλα(ω)induced by a kernel function φ(z,·)∈F∞αbetween Fock spaces.For 1 ≤ p ≤ ∞,they prove that Sφ:F1α→ Fpα is bounded if and only if supa∈C||Sφka||p,α＜∞,(†)where ka is the normalized reproducing kernel of F2α;and,Sφ:F1α → Fpα is compact if and only if lim|a|→∞||Sφka||p,α=0.When 1＜q ≤∞,it is also proved that the condition(†)is not sufficient for boundedness of Sφ:Fqα → Fpα.In the particular case φ(z,(ω))=eαz(ω)φ(z-(ω))with φ ∈ F2α,for 1 ≤ q＜p＜∞,they show that Sφ:Fpα→Fqα is bounded if and only if φ=0;for 1＜p ≤ q＜∞,they give sufficient conditions for the boundedness or compactness of the operator Sφ:Fpα→ Fqα.
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