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On plate decompositions of cone multipliers

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  23 September 2009

Gustavo Garrigós  and
Andreas Seeger
Gustavo Garrigós
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain; Email: ([email protected])
Andreas Seeger
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA; Email: ([email protected])
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Abstract

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An important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for sharp Lp results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones, averages over finite-type curves in ℝ3 and associated maximal functions. We observe that the range of p in Wolff's inequality, for the conic and the spherical versions, can be improved by using bilinear restriction results. We also use this inequality to give some improved estimates on square functions associated to decompositions of cone multipliers in low dimensions. This gives a new L4 bound for the cone multiplier operator in ℝ3.

Keywords

cone multipliersWolff's inequalityplate decompositions

MSC classification

Secondary: 42B99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 631 - 651
Copyright
Copyright © Edinburgh Mathematical Society 2009