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arXiv · 0910.2751

Global Lp continuity of Fourier integral operators

Sandro Coriasco·Michael Ruzhansky
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Abstract

In this paper we establish global Lp regularity properties of Fourier integral operators. The orders of decay of the amplitude are determined for operators to be bounded on $L^p(\Rn)$, $1<p<\infty$, as well as to be bounded from Hardy space $H^1(\Rn)$ to $L^1(\Rn)$. The obtained results extend local $L^p$ regularity properties of Fourier integral operators established by Seeger, Sogge and Stein (1991) as well as global $L^2(\Rn)$ results of Asada and Fujiwara (1978) and Ruzhansky and Sugimoto (2006), to the global setting of $L^p(\Rn)$. Global boundedness in weighted Sobolev spaces $W^{\sigma,p}_s(\Rn)$ is also established. The techniques used in the proofs are the space dependent dyadic decomposition and the global calculi developed by Ruzhansky and Sugimoto (2006) and Coriasco (1999).

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Sandro Coriasco, Michael Ruzhansky. 2009-10-14. Global Lp continuity of Fourier integral operators. https://doi.org/10.1090/s0002-9947-2014-05911-4

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