Maximal Polynomial Modulations of Singular Radon Transforms

2022/10/31 by Becker, Lars
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.17263

Abstract

We prove L² → 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.

Related

• The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals
• Modulation invariant operators
• A degree one Carleson operator along the paraboloid
• Singular maximal functions and Radon transforms near L¹
• Remarks on the maximal operator and Hilbert transform along variable parabolas