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L p regularity of averages over curves and bounds for associated maximal operators
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 1, February 2007
- pp. 61-103
- 10.1353/ajm.2007.0003
- Article
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We prove that for a finite type curve in â3 the maximal operator generated by dilations is bounded on Lp for sufficiently large p. We also show the endpoint Lp â Lp1/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.