On interpolation of pairs of generalized spaces of Besov type

We investigate generalized spaces of Besov type defined with the help of certain positive infinitely differentiable functions of polynomial growth and describe the $K$-functionals for pairs of $H$-spaces and for the pairs of $B$-spaces. We prove interpolation theorems for spaces with different anisotropy. Spaces of functions of mixed smoothness are characterized as “B-products” and interpolation theorems for these spaces are proved. Moreover, we establish embedding and trace theorems.