Triple Hilbert transforms along polynomial surfaces in R-4

Anthony Carbery; Stephen Wainger; James Wright

Triple Hilbert transforms along polynomial surfaces in R-4

Anthony Carbery, Stephen Wainger, James Wright

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the L-2 boundedness of the triple Hilbert transform along the surface given by the graph of a real polynomial P of three variables. We axe interested in understanding the relationship between the geometric properties of the Newton polyhedron of P and the analytic property of L-2 boundedness.

Original language	English
Pages (from-to)	471-519
Number of pages	49
Journal	Revista matematica iberoamericana
Volume	25
Issue number	2
Publication status	Published - 2009

Keywords / Materials (for Non-textual outputs)

Triple Hilbert transform
Newton polyhedron
van der Corput’s lemma
Littlewood-Paley operator
oscillatory singular integral
even in column

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Triple Hilbert transforms along polynomial surfaces in R4Accepted author manuscript, 746 KB

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rmi/1255440065

Cite this

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title = "Triple Hilbert transforms along polynomial surfaces in R-4",

abstract = "We investigate the L-2 boundedness of the triple Hilbert transform along the surface given by the graph of a real polynomial P of three variables. We axe interested in understanding the relationship between the geometric properties of the Newton polyhedron of P and the analytic property of L-2 boundedness.",

keywords = "Triple Hilbert transform, Newton polyhedron, van der Corput{\textquoteright}s lemma , Littlewood-Paley operator , oscillatory singular integral , even in column ",

author = "Anthony Carbery and Stephen Wainger and James Wright",

year = "2009",

language = "English",

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pages = "471--519",

journal = "Revista matematica iberoamericana",

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AU - Carbery, Anthony

AU - Wainger, Stephen

AU - Wright, James

PY - 2009

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AB - We investigate the L-2 boundedness of the triple Hilbert transform along the surface given by the graph of a real polynomial P of three variables. We axe interested in understanding the relationship between the geometric properties of the Newton polyhedron of P and the analytic property of L-2 boundedness.

KW - Triple Hilbert transform

KW - Newton polyhedron

KW - van der Corput’s lemma

KW - Littlewood-Paley operator

KW - oscillatory singular integral

KW - even in column

UR - https://www.scopus.com/pages/publications/70349448101

M3 - Article

SN - 0213-2230

VL - 25

SP - 471

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JO - Revista matematica iberoamericana

JF - Revista matematica iberoamericana

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ER -

Triple Hilbert transforms along polynomial surfaces in R-4

Abstract

Keywords / Materials (for Non-textual outputs)

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Other files and links

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Degenerate Oscillatory Integral Operators

Cite this

Triple Hilbert transforms along polynomial surfaces in R-4

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Other files and links

Fingerprint

Projects

Degenerate Oscillatory Integral Operators

Cite this