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

TL;DR

This paper proves the weak (2,2) boundedness of the quadratic Carleson operator using a novel time-frequency analysis approach for polynomial phase functions of degree two.

Contribution

Introduces a new method for analyzing the quadratic Carleson operator, establishing its weak type (2,2) boundedness.

Findings

Quadratic Carleson operator is of weak type (2,2)

New time-frequency analysis approach for quadratic phases

Advances understanding of polynomial phase operators

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.