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L p regularity of averages over curves and bounds for associated maximal operators
M Pramanik, Andreas Seeger
Source abstract
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.
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