Pseudodifferential operators in function spaces with exponential weights

This paper is a continuation of [17]. We study weighted function spaces of type B-pq(s)(u) and F-pq(s)(u) on the Euclidean space R-n, where u is a wei ght function of at most exponential growth. In particular, u(x) = exp(+/-\x \) is an admissible weight. We consider symbols which belong to the Hormand er class S-1,delta(mu), where mu is an element of R and 0 less than or equa l to delta less than or equal to 1. We give sufficient conditions for the b oundedness of the corresponding pseudodifferential operators in the above f unction spaces. As a main tool, we use molecular decompositions of these sp aces. Furthermore, we prove that the spaces B-pq(s)(u) and F-pq(s)(u) have the lift property.