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We determine certain classes M(X ,q0 (wo), Y 11 (w1 )) of Fourier multipliers between weighted anisotropic Besov and Triebel spaces X, ,0 (wa) and 1' 11 ,qj (wi ) where p0 < 1 and w0 , w1 are weight functions of polynomial growth. To this end we refine a method based on discrete characterizations of function spaces which was introduced in Part I of the paper. Thus widely generalized versions of known results of Bui, Johnson and others are obtained in a unified way.

Fourier Multipliers between Weighted Anisotropic Function Spaces. Part I: Besov Spaces