A Note on the Polynomial Carleson Operator in higher dimensions

We prove the $L^p$-boundedness, $1<p<\mathrm{\infty }$, of the Polynomial Carleson operator in general dimension. This follows the author’s resolution of the one dimensional case as well as the work of Zorin-Kranich on the higher dimensional case in the setting $2\le p<\mathrm{\infty }$. The techniques used in this paper are direct adaptations and natural extensions to the higher dimensional case of the one-dimensional methods developed by the author.