J. Aust. Math. Soc.  76 (2004), 1-21
The weak-type $(1, 1)$ of Fourier integral operators of order $-(n-1)/2$

Terence Tao
  Department of Mathematics
  UCLA
  Los Angeles CA 90024
  USA
  tao@math.ucla.edu


Abstract
Let $T$ be a Fourier integral operator on $\mathbb{R}^n$ 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.
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