Resolvent estimates for Fleming-Viot operators with Brownian drift

This article is a supplement to the paper of D. A. Dawson and P. March (J. funet. Anal. 132 (1995), 417-472). We define a two-parameter scale of Banac h spaces of functions defined on M-1(R-d), the space of probability measure s on d-dimensional euclidean space, using weighted sums of the classical So bolev norms. We prove that the resolvent of the Fleming-Viot operator with constant diffusion coefficient and Brownian drift acts boundedly between ce rtain members of the scale. These estimates gauge the degree of smoothing p erformed by the resolvent and separate the contribution due to the diffusio n coefficient and that due to the drift coefficient. (C) 1998 Academic Pres s.