Pseudodifferential Operators in Function Spaces with Exponential Weights

This paper is a continuation of [17]. We study weighted function spaces of type B a pq ( u ) and F a pq ( u ) on the Euclidean space ℝ n , where u is a weight function of at most exponential growth. In particular, u(x) = exp(±| x |) is an admissible weight. We consider symbols which belong to the Hörmander class S u 1,δ , where u ∈ ℝ and 0 ≤ δ ≤ 1. We give sufficient conditions for the boundedness of the corresponding pseudodifferential operators in the above function spaces. As a main tool, we use molecular decompositions of these spaces. Furthermore, we prove that the spaces B a pq ( u ) and F a pq ( u ) have the lift property.