Multi-Linear Singular Integrals

Cornell University, Ithaca NY

Investigators

Abstract

Over the past two years I have been working on multi-linear singular integral operators. Recently, in a joint work with T.Tao and C.Thiele we generalized the previous results on the bilinear Hilbert transform to the case of multilinear operators with much more singular symbols. The striking fact about these developments is that it seems that these techniques could have a very nice and important application to the spectral theory of Schroedinger operators. The final goal of our project, is to show that for the classical Schroedinger operators with square integrable potential and for almost every positive eigenvalue, their corresponding eigenfunctions are bounded. The answer to the above conjecture would imply a better understanding of the behaviour of the Schroedinger operators, which lie in the heart of Quantum Mechanics.