Abstract:
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.
Keywords and phrases:spaces of Besov type, spaces of Sobolev–Liouville type, spaces of functions of mixed smoothness, interpolation, $K$-functional, “B-product”, embeddings, traces.
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