2010•Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)Requires access
Spaces of functions with dominating mixed properties of smoothness as B-products
A. G. Baghdasaryan
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Abstract
It is proved, that certain known function spaces (such as S B, S F spaces of functions of mixed smoothness and approximation spaces A ) 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 B spaces are proved using B-products and covering method. It is proved that space S B is a “real” method interpolation space for the pair of corresponding spaces of Nikolskii-Besov type.