Remarks on the maximal operator and Hilbert transform along variable parabolas

Abstract

We prove the boundedness of the maximal operator and Hilbert transform along certain variable parabolas in $L^p$ for $p>p_0$ with some $p_0\in (1,2)$. Connections with the Hilbert transform along vector fields and the polynomial Carleson's maximal operator are also discussed.

arXiv comment11 pages