We consider a class of Fourier integral operators, globally dened on R^d, with symbols and phases satisfying product type estimates (the so-called SG or scattering classes). We prove a sharp continuity result for such operators when acting on the modulation spaces Mp. The minimal loss of derivatives is shown to be d|1/2-1/p|. This global perspective produces a loss of decay as well, given by the same order. Strictly related, striking examples of unboundedness on L^p spaces are presented.
On the Global Boundedness of Fourier IntegralOperators
CORDERO, Elena;RODINO, Luigi Giacomo
2010-01-01
Abstract
We consider a class of Fourier integral operators, globally dened on R^d, with symbols and phases satisfying product type estimates (the so-called SG or scattering classes). We prove a sharp continuity result for such operators when acting on the modulation spaces Mp. The minimal loss of derivatives is shown to be d|1/2-1/p|. This global perspective produces a loss of decay as well, given by the same order. Strictly related, striking examples of unboundedness on L^p spaces are presented.
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