Two problems on maximal functions and singular integrals; Averages over curves and related maximal functions

speaker: Andreas Seeger (University of Wisconsin-Madison)

abstract: Talk 1: Two problems on maximal functions and singular integrals. (a) Given a Hörmander-Mikhlin multiplier m, when does the maximal function $\sup_{t>0}
\Cal F^{-1}m\widehat f
$ define a bounded operator on $L^p$? We present recent joint work with M. Christ, P. Honzik, L. Grafakos on this problem.

Talk 2: Averages over curves and related maximal functions. We discuss sharp Lp Sobolev regularity results for averaging over curves in three dimensions, as well as results maximal functions generated by dilates of such curves. This is joint work with Malabika Pramanik.

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