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Maximal polynomial modulations of singular integrals

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arxiv 1711.03524 v6 pith:RZ3U33E5 submitted 2017-11-09 math.CA

classification math.CA
keywords polynomialboundedcarlesonmathbbmathbfmaximaltheoremcalder
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abstract

Let $K$ be a standard H\"older continuous Calder\'on--Zygmund kernel on $\mathbb{R}^{\mathbf{d}}$ whose truncations define $L^2$ bounded operators. We show that the maximal operator obtained by modulating $K$ by polynomial phases of a fixed degree is bounded on $L^p(\mathbb{R}^{\mathbf{d}})$ for $1 < p < \infty$. This extends Sj\"olin's multidimensional Carleson theorem and Lie's polynomial Carleson theorem.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals

    math.CA 2019-08 accept novelty 7.0 of 10

    For every p in (1, infinity), the maximal modulation of the line-restricted Hilbert transform along the parabola is bounded on Lp, uniformly over all lines.

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