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GLOBAL L p CONTINUITY OF FOURIER INTEGRAL OPERATORS
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Journal Article
GLOBAL L p CONTINUITY OF FOURIER INTEGRAL OPERATORS
2014
Overview
In this paper we establish global Lp(ℝn)-regularity properties of Fourier integral operators. The orders of decay of the amplitude are determined for operators to be bounded on Lp(ℝn), 1 < p < ∞, as well as to be bounded from Hardy space H¹(ℝn) to L¹(ℝn). This extends local Lp-regularity properties of Fourier integral operators, as well as results of global L²(ℝn) boundedness, to the global setting of Lp(ℝn). Global boundedness in weighted Sobolev spaces ${\\mathrm{W}}_{\\mathrm{s}}^{\\mathrm{\\sigma },\\mathrm{p}}\\left({\\mathrm{\\mathbb{R}}}^{\\mathrm{n}}\\right)$ is also established, and applications to hyperbolic partial differential equations are given.
Publisher
American Mathematical Society
