This proposal deals with problems related to oscillatory integrals, several complex variables, singular integral operators, mathematical physics, boundary-value problems, Hardy space theory, and the interrelation of these topics. The proposal involves also intense collaboration with a group of mathematicians at Princeton and at other institutions, including the mentoring of doctoral students and postdoctoral associates. In particular, Professor Stein will continue his work on singular Radon transforms and oscillatory integrals, multi-parameter harmonic analysis, Fourier integral operators, and Hardy spaces and boundary-value problems for the Laplace operator. Professor Fefferman will continue working on asymptotic formulas for the ground-state energy of a large atom, nodal sets and eigenfunctions for the Laplace operator, conformal invariants, and delta-bar problems in several complex variables.
