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The purpose of this paper is to establish a very general Cameron-Storvicktheorem involving the generalized analytic Feynman integral of functionals onthe product function space $C_{a,b}^2[0,T]$. The function space $C_{a,b}[0,T]$can be induced by the generalized Brownian motion process associated withcontinuous functions $a$ and $b$. To do this we first introduce the class$\mathcal F_{A_1,A_2}^{\,\,a,b}$ of functionals on $C_{a,b}^2[0,T]$ which is ageneralization of the Kallianpur and Bromley Fresnel class $\mathcalF_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick type theorem onthe product function space $C_{a,b}^2[0,T]$.  Finally we use our Cameron--Storvick type theorem to obtain severalmeaningful results and examples.

A Cameron-Storvick type theorem on $C_{a,b}^2[0,T]$ with applications