WEIGHTED PARABOLIC TRIEBEL SPACES OF PRODUCT TYPE - FOURIER MULTIPLIERS AND PSEUDODIFFERENTIAL-OPERATORS

The aim of the paper is a detailed study of the boundedness properties of Fourier multipliers and pseudo-differential operators on weighted parabolic Triebel spaces of product type. We prove estimates for Fourier multipliers of Hormander-Michlin-Marcinkiewicz type on weighted and unweighted Triebel spaces, L(p)-spaces and vector-valued L(p)-spaces. The same method is then applied to obtain estimates for pseudo-differential operators in several generalizations of the Hormander class S1,delta-m and their adjoints.