Domains of type 1,1 operators: a case for Triebel-Lizorkin spaces

Pseudo-differential operators of type 1, 1 are proved continuous from the Triebel-Lizorkin F-p,1(d) to L-p, 1 less than or equal to p < infinity, when of order d. and this is, in general, the largest possible domain among the Besov and Triebel-Lizorkin spaces. Hormander's condition on the twisted diagonal is extended to this framework, using a general support rule for Fourier transformed pseudodifferential operators. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.