The weak-type (1,1) of Fourier integral operators of order –( n –1)/2

Source abstract

Abstract Let T be a Fourier integral operator on R n of order–( n –1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H 1 to L 1 . In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.