Degenerate convolution equations in vector-valued weighted Besov spaces

In a series of recent publications, Fourier multiplier theorems with operator-valued multiplier functions have found many applications. From this point of view Besov spaces form one class of function spaces which are of special interest. In the present paper B􀀀separability properties of degenerate convolution differential-operator equations with unbounded operator coefficients in vector-valued weighted Besov spaces are investigated. These results are applied to obtain the maximal B􀀀regularity properties for anisotropic integro-differential equations and many convolution equations