Department of Mathematics
Colloquium
by
Prof. Roger L. Jones

The talk will include a discussion of the properties and applications of these operators, as well as a discussion of the Calderón-Zygmund decomposition, which plays a key role in the proofs.

The talk will be largely self contained, and should be understandable to first year graduate students. The best references related to this talk are to papers that are still in press, but for background, the following papers could be consulted: (Reference [2] is partly expository, and is available from the New York Journal web site.)

1. Gaposkhin, V., A theorem on the convergence almost everywhere of a sequence of measurable functions and its applications, Math. USSR Sbornik 33 (1977) 1-17.
2. Jones, Roger L., Ergodic theory and connections with analysis and probability, New York J. of Math., 3A (1997) 31-67.
3. Jones, Roger L., Ostrovskii, I., and Rosenblatt, J., Square functions in ergodic theory, Ergodic Theory and Dyn. Sys., 16 (1996) 267-305.