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

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

2005-01-11

arxiv.org/abs/math/0501165v1

American Journal of Mathematics, 129, no.1 (2007), 61-103.

Mathematics

Classical Analysis and ODEs

Scientific paper

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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