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arXiv · 1510.03807

Global regularity properties for a class of Fourier integral operators

Michael Ruzhansky·Mitsuru Sugimoto
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Abstract

While the local $L^p$-boundedness of nondegeneral Fourier integral operators is known from the work of Seeger, Sogge and Stein, not so many results are available for the global boundedness on $L^p(\mathbb R^n)$. In this paper we give a sufficient condition for the global $L^p$-boundedness for a class of Fourier integral operators which includes many natural examples. We also describe a construction that can be used to deduce global results from the local ones. An application is given to obtain global $L^p$-estimates for solutions to Cauchy problems for hyperbolic partial differential equations.

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Michael Ruzhansky, Mitsuru Sugimoto. 2015-10-12. Global regularity properties for a class of Fourier integral operators. https://arxiv.org/abs/1510.03807

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