A local smoothing estimate in higher dimensions

2002/05/07 by I. Laba, Laba, I., T. Wolff +1 · 2 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.math/0205059

25 pages

arxiv created 2002/05/07 · arxiv updated 2009/11/30

Abstract

We prove the higher-dimensional analogue of Wolff's local smoothing estimate (Geom. Funct. Anal. 2001) for large p. As in the 2+1-dimensional case, the estimate is sharp for any given value of p, but it is likely that the range of p can be improved.

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• Local smoothing and maximal estimates for average over surfaces of codimension 2 in \mathbb R⁴

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