Global regularity properties for a class of Fourier integral operators

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.

15 pages

References in corpus (3)

• Estimates for rough Fourier integral and pseudodifferential operators and applications to the boundedness of multilinear operators
• Global and local regularity of Fourier integral operators on weighted and unweighted spaces
• A smoothing property of Schrodinger equations in the critical case