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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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How to Go beyond the Case hlin(φ‎) ≥ 5

How to Go beyond the Case hlin(φ‎) ≥ 5

(p.131) Chapter Seven How to Go beyond the Case hlin(φ‎) ≥ 5
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Isroil A. Ikromov

Detlef Müller

Princeton University Press

This chapter mostly considers the domains of type Dsubscript (l), which are in some sense “closest” to the principal root jet, since it turns out that the other domains Dsubscript (l) with l ≥ 2 are easier to handle. In a first step, by means of some lower bounds on the r-height, this chapter establishes favorable restriction estimates in most situations, with the exception of certain cases where m = 2 and B = 3 or B = 4. In some cases the chapter applies interpolation arguments in order to capture the endpoint estimates for p = psubscript c. Sometimes this can be achieved by means of a variant of the Fourier restriction theorem. However, in most of these cases the chapter applies complex interpolation in a similar way as has been done in Chapter 5.

Keywords:   r-height, restriction estimates, interpolation arguments, endpoint estimates, Fourier restriction theorem, complex interpolation, normalized measures, spectral localization, open cases

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