L Regularity of Averages over Curves and Bounds for Associated Maximal Operators
نویسنده
چکیده
We prove that for a finite type curve in R the maximal operator generated by dilations is bounded on Lp for sufficiently large p. We also show the endpoint Lp → L 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.
منابع مشابه
LP REGULARITY OF AVERAGES OVER CURVES AND BOUNDS FOR ASSOCIATED MAXIMAL OPERATORS By MALABIKA PRAMANIK and ANDREAS SEEGER
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 → L 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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تاریخ انتشار 2005