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

DOI10.1017/S1446788700008661zbMATH Open1059.42013arXivmath/0201220OpenAlexW2008219820MaRDI QIDQ4820568

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Publication date: 15 October 2004

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Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math/0201220

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