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L^p regularity of averages over curves and bounds for associated maximal operators
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classification
math.CAmath.AP
keywords
largemaximaloperatorsregularityresultassociatedaveragesaveraging
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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