In this paper, the authors characterize pointwise multipliers for Campanato spaces on the Gauss measure space (ℝn,| · |,γ), which includes BMO(γ) as a special case. As applications, several examples of the pointwise multipliers are given. Also, the authors give an example of a nonnegative function in BMO(γ) but not in BLO(γ).

To form Riemann sums for generalized Riemann integrals, the domain of integration must be partitioned in a suitable manner. The existence of the required partitions is usually proved by a simple method of repeated bisection of the domain of integration. However, when the domain is the Cartesian product of infinitely many copies of the set of real numbers, this simple method of proof has frequently failed. A proof which works for infinite-dimensional spaces is provided here.

We consider integrals on Wiener space of the forms E(exp K(x)) and E(exp K(x) |L(x) = l) where K is a quadratic form and L a system of linear forms. We give explicit formulas for these integrals in terms of the operators K and L, in the case that these arise from quasilinear functions in the sense of Zhao (1981). As examples, we recover Lévy's area formula in the plane, and derive new formulas for the probability density of the radius of gyration tensor for Brownian paths.