A polynomial Carleson operator along the paraboloid

  title={A polynomial Carleson operator along the paraboloid},
  author={L. B. Pierce and Po-Lam Yung},
  journal={Revista Matem{\'a}tica Iberoamericana},
In this work we extend consideration of the polynomial Carleson operator to the setting of a Radon transform acting along the paraboloid in $\mathbb{R}^{n+1}$ for $n \geq 2$. Inspired by work of Stein and Wainger on the original polynomial Carleson operator, we develop a method to treat polynomial Carleson operators along the paraboloid via van der Corput estimates. A key new step in the approach of this paper is to approximate a related maximal oscillatory integral operator along the… 
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