The (weak-$L^2$) Boundedness of The Quadratic Carleson Operator

Abstract

We prove that the generalized Carleson operator with polynomial phase function of degree two is of weak type (2,2). For this, we introduce a new approach to the time-frequency analysis of the quadratic phase.

48 pages, 9 figures. Final version, to appear in GAFA. Minor typos corrected, additional explanations given