Journal of the Australian Mathematical Society

Research Article

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

Terence Taoa1

a1 Department of Mathematics, UCLA, Los Angeles CA 90024, USA e-mail: tao@math.ucla.edu

Abstract

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.

(Received February 15 2002)

(Revised November 28 2002)

2000 Mathematics subject classification

  • primary 42B20