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

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

2002-01-23

arxiv.org/abs/math/0201220v2

Mathematics

Classical Analysis and ODEs

17 pages, no figures, to appear, J. Aust. Math. Soc. Minor grammatical changes and some more references added

Scientific paper

Let $T$ be a Fourier integral operator on $\R^n$ of order $-(n-1)/2$. It was
shown by Seeger, Sogge, and Stein that $T$ mapped 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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