Global $L^p$ continuity of Fourier integral operators

By Sandro Coriasco, Michael Ruzhansky. Transactions of the American Mathematical Society, 2009

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In this paper we establish global L-p(R-n)-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 < infinity, as well as to be bounded from Hardy space H-1(R-n) to L-1(R-n). This extends local L-p-regularity properties of Fourier integral operators, as well as results of global L-2(R-n) boundedness, to the global setting of L-p(R-n). Global boundedness in weighted Sobolev spaces W-s(sigma,p) (R-n) is also established, and applications to hyperbolic partial differential equations are given.

Subfields: Applied Mathematics

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