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L^p regularity of averages over curves and bounds for associated maximal operators

Malabika Pramanik·Andreas Seeger
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Abstract

We prove that for a finite type curve in $\mathbb R^3$ the maximal operator generated by dilations is bounded on $L^p$ for sufficiently large $p$. We also show the endpoint $L^p \to L^{p}_{1/p}$ regularity result for the averaging operators for large $p$. The proofs make use of a deep result of Thomas Wolff about decompositions of cone multipliers.

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Malabika Pramanik, Andreas Seeger. 2005-01-11. L^p regularity of averages over curves and bounds for associated maximal operators. https://arxiv.org/abs/math/0501165

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