Weighted norm inequalities for oscillatory integrals with finite type phases on the line

Details Weighted norm inequalities for oscillatory integrals with finite type phases on the line Weighted norm inequalities for oscillatory integrals with finite type phases on the line

2011-10-27

arxiv.org/abs/1110.6031v1

Mathematics

Classical Analysis and ODEs

22 pages

Scientific paper

We obtain two-weighted $L^2$ norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type. The conditions imposed on the weights involve geometrically-defined maximal functions, and the inequalities are best-possible in the sense that they imply the full $L^p(\mathbb{R})\rightarrow L^q(\mathbb{R})$ mapping properties of the oscillatory integrals. Our results build on work of Carbery, Soria, Vargas and the first author.

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