On plate decompositions of cone multipliers

Details On plate decompositions of cone multipliers On plate decompositions of cone multipliers

2007-07-13

arxiv.org/abs/0707.1934v2

Proceedings of the Edinburgh Mathematical Society, 52 (2009), 1-21.

Mathematics

Classical Analysis and ODEs

This is the revised version to appear in the proceedings of the Edinburgh Mathematical Society

Scientific paper

An important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for a variety of problems in harmonic analysis. We observe that the range 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 L^4 bound for the cone multiplier operator in three dimensions.

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