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## Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

*Isroil A. Ikromov and Detlef Müller*

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.001.0001
- Subject:
- Mathematics, Geometry / Topology

This is the first book to present a complete characterization of Stein–Tomas-type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all ... More

## Introduction

*Isroil A. Ikromov, Detlef Müller, Isroil A. Ikromov, and Detlef Müller*

### in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.003.0001
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses the Fourier restriction. The Fourier restriction problem presents one important instance of a wide circle of related problems, such as the boundedness properties of Bochner ... More

##
Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in ^{R}3, and Newton Polyhedra *Detlef Müller*

*Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)*

### in Advances in Analysis: The Legacy of Elias M. Stein

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159416
- eISBN:
- 9781400848935
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159416.003.0013
- Subject:
- Mathematics, Numerical Analysis

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 ... More

##
How to Go beyond the Case *h*lin(φ) ≥ 5

*Isroil A. Ikromov and Detlef Müller*

### in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.003.0007
- Subject:
- Mathematics, Geometry / Topology

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 ... More

## Reduction to Restriction Estimates near the Principal Root Jet

*Isroil A. Ikromov and Detlef Müller*

### in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.003.0003
- Subject:
- Mathematics, Geometry / Topology

This chapter shows that one may reduce the desired Fourier restriction estimate to a piece Ssubscript Greek small letter psi of the surface S lying above a small, “horn-shaped” neighborhood ... More

## On Oscillatory Integral Operators in Higher Dimensions

*Jean Bourgain*

*Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)*

### in Advances in Analysis: The Legacy of Elias M. Stein

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159416
- eISBN:
- 9781400848935
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159416.003.0003
- Subject:
- Mathematics, Numerical Analysis

This chapter discusses the progress made towards problems originating from Stein's seminal paper, “Some problems in harmonic analysis.” It is by now well-known that the mapping properties of Fourier ... More

## Auxiliary Results

*Isroil A. Ikromov and Detlef Müller*

### in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter compiles various auxiliary results; including variants of van der Corput-type estimates for one-dimensional oscillatory integrals and related sublevel estimates through “integrals of ... More

## Maximal Function; Bounding Averages and Pointwise Convergence

*Ali Taheri*

### in Function Spaces and Partial Differential Equations: Volume 2: Contemporary Analysis

- Published in print:
- 2015
- Published Online:
- September 2015
- ISBN:
- 9780198733157
- eISBN:
- 9780191797729
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198733157.003.0013
- Subject:
- Mathematics, Analysis

This chapter introduces the Hardy-Littlewood maximal functions and establishes its bounded properties in various Lebesgue and Marcinkiewicz type spaces. The chapter also presents many applications to ... More

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