Maximal Polynomial Modulations of Singular Radon Transforms

Abstract

We prove $L^2\to L^p$ estimates on the torus for maximal polynomial modulations of Calderón-Zygmund operators with anisotropic scaling. We obtain improved constants in these estimates. As a corollary, maximal polynomial modulations of a mollified version of the Hilbert transform along the parabola are bounded with only logarithmic dependence of the estimate on the Lipschitz constant of the mollifier.

arXiv commentsmall corrections following referee report