by A. G. Baghdasaryan
Preprint series: 03-10, Reports on Analysis
Abstract: We investigate generalized spaces of Besov type defined by some positive infinitely differentiable functions of polynomial growth and determine the K-functional for pairs of this type of H- and 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 theorems and a trace theorem.
Keywords: Spaces of Sobolev and Besov type, spaces with dominating mixed smoothness, real interpolation, K-functional, embeddings, traces