Spaces of functions with dominating mixed properties of smoothness as B-products

摘要

It is proved, that certain known function spaces (such as S_(p,q)~sB, S_(p,q)~s spaces of functions of mixed smoothness and approximation spaces A_(p,q)~s) can be characterized in terms of spaces of Sobolev-Liouville and Nikolskii-Besov type spaces and so called "B-products". The representation theorems of S_(p,q)~sB spaces are proved using B-products and covering method. It is proved that space S_(p,q)~sB is a "real" method interpolation space for the pair of corresponding spaces of Nikolskii-Besov type.