Abstract. In this paper we develop an Lp Fourier-Feynman theory for a class of functionals on Wiener space of the form F(x) = f(J0 axdx, ... , /0 a"dx). We then define a convolution product for functionals on Wiener space and show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms.

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Yen's inversion formula for conditional Wiener integrals is very complicated to apply when the conditioning function is vector-valued. This paper gives a very simple formula for such integrals. In particular, we express the conditional Wiener integral directly in terms of an ordinary (i.e., nonconditional) Wiener integral. Using this new formula, it is very easy to generalize the Kac-Feynman formula and also to obtain a Cameron-Martin type translation theorem for general conditional Wiener integrals.

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