Abstract
We show that entire functions $$\varphi $$ , which induce bounded products of Volterra integral operators $$V_g$$ (Volterra companion operators $$J_g$$ ) and composition operators $$C_{\varphi }$$ acting between different Fock spaces, must be affine functions, i.e. $$\varphi (z) = az + b$$ . Then, using this special form of $$\varphi $$ , we characterize boundedness and compactness of these products in term of new quantities, which are much simpler than the Berezin type integral transforms in the previous papers.
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