Paraproducts With Flag Singularities

Cornell University, Ithaca NY

Investigators

Abstract

DMS - 0355360 Camil Muscalu Cornell University Paraproducts with Flag Singularities Abstract Over the last few years we have been working on developing further the theory of multilinear singular integrals and their Carleson-type maximal analogs, in connection with the spectral theory of one-dimensional Schroedinger operators. We understood many of its beautiful features, but still much more work needs to be done The present Project is focused on creating a consistent multi-parameter theory for these multilinear operators. The motivation for such a study is not only our previous work, but also the desire of analysts of having a general Kato-Ponce theory, so useful in PDE. Some of these operators have a very special multi-parameter structure not seen among the previously studied operators in harmonic analysis. Understanding their combinatorics is a deep and challenging study. Our plan is to handle not only large classes of such paraproducts with "flag singularities", but also "analytic series" of such operators. We believe that these new techniques will have a broad impact to several problems in nonlinear analysis.