A local-to-global weak (1,1) type argument and applications to Fourier integral operators

Abstract

In this work we provide a criterion for the global weak (1,1) type of integral operators which are known to be locally uniformly of weak (1,1) type. As an application, we establish the global weak (1,1) type for a class of Fourier integral operators. While the local result is known from the work of Tao [33] for Fourier integral operators of order $-(n-1)/2,$ we give natural sufficient conditions in order to extend it to the corresponding global estimate