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

By M. Pramanik, Andreas Seeger. 2005

92 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f61f3b2c1577c7b8c3dd75a4ef652b94fe52f2a2

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In Applied Mathematics

Citations in the corpus

The proof of the l 2 Decoupling Conjecture (2015, background): “The following argument is sketched in [21] and was worked out in detail for conical surfaces in [27].”
On plate decompositions of cone multipliers (2007, methodology): “This can be achieved by using scaling and induction on scales arguments such as in §2 of [16], see also the article by Laba and Pramanik [10] for related results.”
Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, background): “The relevant machinery that we now call decouplings showed its initial potential for applications in papers such as [17], [14], [16] and [4].”
A sharp square function estimate for the cone in ℝ3 (2019, background): “Similar ideas can also be traced back to the iteration argument of Pramanik-Seeger [21]).”