The weak-type (1,1) of Fourier integral operators of order –(<i>n</i>–1)/2

Terence Tao

Type: Article

Publication Date: 2004-02-01

Citations: 43

DOI: https://doi.org/10.1017/s1446788700008661

Abstract

Abstract Let T be a Fourier integral operator on R n of order–( n –1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H 1 to L 1 . In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.

Locations

Journal of the Australian Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF
Journal of the Australian Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF
Journal of the Australian Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - PDF

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Works Cited by This (8)

Action	Title	Year	Authors
+	Averages of functions over hypersurfaces in ? n	1985	Christopher D. Sogge Elias M. Stein
+	Regularity Properties of Fourier Integral Operators	1991	Andreas Seeger Christopher D. Sogge Elias M. Stein
+ PDF	A parametrix construction for wave equations with $C^{1,1}$ coefficients	1998	Hart F. Smith
+	Damped Oscillatory Integral Operators with Analytic Phases	1998	D. H. Phong E. M. Stein
+	Singularities of affine fibrations in the regularity theory of Fourier integral operators	2000	Michael Ruzhansky
+	Lp estimates for the wave equation	1980	Juan Carlos Peral
+	Damping oscillatory integrals	1990	Michael Cowling Shaun Disney Giancarlo Mauceri Detlef M�ller
+	L[p] estimates for the wave equation	1978	Juan Carlos Peral