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Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)$
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Isroil A. Ikromov and Detlef Müller

Print publication date: 2016

Print ISBN-13: 9780691170541

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691170541.001.0001

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Restriction for Surfaces with Linear Height below 2

Restriction for Surfaces with Linear Height below 2

Chapter:
(p.57) Chapter Four Restriction for Surfaces with Linear Height below 2
Source:
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)
Author(s):

Isroil A. Ikromov

Detlef Müller

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691170541.003.0004

This chapter studies the case where hsubscript lin(φ‎) < 2. It first performs a dyadic decomposition of a domain introduced in the previous chapter and the corresponding measure dμ‎superscript Greek small letter rho1. Next, given a measure dν‎ₖ, the chapter performs yet another Littlewood–Paley decomposition. Since the decay of the Fourier transforms of these measures is strongly nonisotropic, as a last step this chapter performs a dyadic decomposition in each of the frequency variables ζ‎₁, ζ‎₂, and ζ‎₃ dual to x₁, x₂, and x₃. In the end, a few cases in which this chapter is unable to sum the operator norms remain open, to be dealt with in the next chapter.

Keywords:   restriction, dyadic decomposition, Littlewood–Paley decomposition, operator norms, normalized rescale measures, restriction estimates

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