CBMS Regional Conference Series in Mathematics 1989; 49 pp; softcover Number: 70 ISBN10: 0821807218 ISBN13: 9780821807217 List Price: US$24 Member Price: US$19.20 All Individuals: US$19.20 Order Code: CBMS/70
 This book is based on lectures presented by the author at DePaul University in July 1986. The lectures cover three main topics. The first is local time theory for Brownian motion and some geometrical inequalities for harmonic functions in the upper halfplane \(R^{n+1}_+\). The author sketches a proof of the inequalities obtained by Barlow and Yor for the maximal local time functional. The second topic concerns a probabilistic treatment of Riesz transforms in \(R^{n+1}_+\), and semimartingale inequalities. The author proves semimartingale inequalities of the type usually obtained for martingales. The final topic centers on a discussion of the OrnsteinUhlenbeck semigroup and P. A. Meyer's extension of the Riesz inequalities for the infinitedimensional version of this semigroup. One of the major results of the book is the establishment of inequalities for the density of the area integral. Readership Table of Contents  The BarlowYor inequalities
 The density of the area integral
 Norm inequalities for \(D\)
 Local estimates
 Terminal expectations and singular integrals
 The OrnsteinUhlenbeck semigroup
 P. A. Meyer's Riesz transform inequalities
 The OrnstienUhlenbeck process for the Rademacher functions
