Abstract
Let K be a standard Hölder continuous Calderón–Zygmund kernel on Rd whose truncations define L2 bounded operators. We show that the maximal operator obtained by modulating K by polynomial phases of a fixed degree is bounded on Lp(Rd) for 1<p<∞. This extends Sjölin's multidimensional Carleson theorem and Lie's polynomial Carleson theorem.
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