Jump to ContentJump to Main Navigation
Advances in AnalysisThe Legacy of Elias M. Stein$
Users without a subscription are not able to see the full content.
Advances in Analysis: The Legacy of Elias M. Stein

Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger

Print publication date: 2014

Print ISBN-13: 9780691159416

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159416.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 07 December 2021

Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller

Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller

Chapter:
(p.303) Chapter Thirteen Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller
Source:
Advances in Analysis
Author(s):
Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159416.003.0013

This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a smooth, finite type hypersurface in R³ with Riemannian surface measure dσ‎). The first problem is a classical question about estimates for oscillatory integrals, and there exists a huge body of results on it, in particular for convex hypersurfaces. The other two problems had first been formulated by Stein: the study of maximal averages along hypersurfaces has been initiated in Stein's work on the spherical maximal function, and also the idea of Fourier restriction goes back to him.

Keywords:   harmonic analysis, finite-type hypersurfaces, Newton polyhedra, oscillatory integrals, convex hypersurfaces, maximal averages, spherical maximal function, Fourier restriction

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.