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

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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} ightarrow L^q\mathbb{R}\$ mapping properties of the oscillatory integrals. Our results build on work of Carbery, Soria, Vargas and the first author.

Autor: Jonathan Bennett; Samuel Harrison

Fuente: https://archive.org/