A local-to-global boundedness argument and Fourier integral operators

Abstract

We give a criterion for the global boundedness of integral operators which are known to be locally bounded. As an application, we discuss the global $L^p$-boundedness for a class of Fourier integral operators. While the local $L^p$-boundedness of Fourier integral operators is known from the work of Seeger, Sogge and Stein, not so many results are available for the global boundedness on $L^p({\mathbb{R}}^n)$. We give several natural sufficient conditions for them.

13 pages. This paper is a substantially reworked version of our paper arXiv:1510.03807, where we now deduce the result of that paper on the global boundedness for Fourier integral operators from a much more general principle for integral operators

References in corpus (1)

• Global and local regularity of Fourier integral operators on weighted and unweighted spaces