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

Published online by Cambridge University Press:  09 April 2009

Terence Tao
Affiliation:
Department of Mathematics, UCLA, Los Angeles CA 90024, USA e-mail: tao@math.ucla.edu
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Abstract

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Let T be a Fourier integral operator on Rn of order–(n–1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H1 to L1. 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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

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