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

Abstract

We prove that for a finite type curve in ℝ3 the maximal operator generated by dilations is bounded on Lp for sufficiently large p. We also show the endpoint Lp → 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.