Triple Hilbert transforms along polynomial surfaces in $\mathbb{R}^4$

Anthony Carbery, Stephen Wainger, James Wright

Type: Article

Publication Date: 2009-08-31

Citations: 3

DOI: https://doi.org/10.4171/rmi/573

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 are interested in understanding the relationship between the geometric properties of the Newton polyhedron of P and the analytic property of L^2 boundedness.

Locations

Revista Matemática Iberoamericana - View - PDF
Project Euclid (Cornell University) - View - PDF

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Works Cited by This (7)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+ PDF Chat	Problems in harmonic analysis related to curvature	1978	Elias M. Stein Stephen Wainger
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+	L 2 Boundedness of Hilbert Transforms Along Surfaces and Convolution Operators Homogeneous with Respect to a Multiple Parameter Group	1977	Alexander Nagel Stephen Wainger
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+ PDF Chat	The estimation of an integral arising in multiplier transformations	1970	Elias Stein Stephen Wainger