Integral Operators Between Fock Spaces

In this paper,the authors study the integral operator■induced by a kernel functionφ(z,·)∈F_α~∞between Fock spaces.For 1≤p≤∞,they prove that S_φ:F_α^(1)→F_α^(p)is bounded if and only if■where k_(a)is the normalized reproducing kernel of F_α^(2);and,S_φ:F_α^(1)→F_α^(p)is compact if and only if■When 1<q≤∞,it is also proved that the condition(?)is not sufficient for boundedness of S_φ:F_α^(q)→F_α^(p).In the particular case■with ■∈F^(2)_α,for 1≤q<p<∞,they show that S_φ:F^(p)_α→F^(q)_αis bounded if and only if■;for 1<p≤q<∞,they give sufficient conditions for the boundedness or compactness of the operator S^(q)_φ:F^(p)_α→F_α.