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arXiv · 1110.6031

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

Jonathan Bennett·Samuel Harrison
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Abstract

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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Jonathan Bennett, Samuel Harrison. 2011-10-27. Weighted norm inequalities for oscillatory integrals with finite type phases on the line. https://arxiv.org/abs/1110.6031

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