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Abstract. We prove variational and jump inequalities for a large class of linear operators arising in harmonic analysis.

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Abstract. We prove that for a finite type curve in R 3 the maximal operator generated by dilations is bounded on L p for sufficiently large p. We also show the endpoint L p → 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.