In this paper we establish global L^p regularity properties of Fourier Integral Operators. The orders of decay of the amplitude are determined for operators to be bounded on L^p(R^n), 1<p<infty, as well as to be bounded from Hardy space H^1(R^n) to L^1(R^n). The obtained results extend local L^p regularity properties of Fourier Integral Operators established by Seeger, Sogge and Stein in 1991, as well as global L^2(R^n) results of Asada and Fujiwara (1978), Coriasco (1999), and Ruzhansky and Sugimoto (2006), to the global setting of L^p(\Rn)$. Global boundedness in weighted Sobolev spaces W^{\sigma,p}_s(R^n) is also established.
Global L^p continuity of Fourier Integral Operators
CORIASCO, Sandro;
2014-01-01
Abstract
In this paper we establish global L^p regularity properties of Fourier Integral Operators. The orders of decay of the amplitude are determined for operators to be bounded on L^p(R^n), 1
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