The weak-type $(1,1)$ of Fourier integral operators of order $-(n-1)/2$
Abstract
Description
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.
17 pages, no figures, to appear, J. Aust. Math. Soc. Minor grammatical changes and some more references added
17 pages, no figures, to appear, J. Aust. Math. Soc. Minor grammatical changes and some more references added