Oscillatory integrals and Fourier transforms of surface carried measures

Authors:
Michael Cowling and Giancarlo Mauceri

Journal:
Trans. Amer. Math. Soc. **304** (1987), 53-68

MSC:
Primary 42B10; Secondary 42B25

DOI:
https://doi.org/10.1090/S0002-9947-1987-0906805-0

MathSciNet review:
906805

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Abstract: We suppose that is a smooth hypersurface in with Gaussian curvature and surface measure , is a compactly supported cut-off function, and we let be the surface measure with . In this paper we consider the case where is the graph of a suitably convex function, homogeneous of degree , and estimate the Fourier transform . We also show that if is convex, with no tangent lines of infinite order, then decays as provided . The techniques involved are the estimation of oscillatory integrals; we give applications involving maximal functions.

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0906805-0

Article copyright:
© Copyright 1987
American Mathematical Society