On the interpolation properties of certain generalized spaces of Besov type

by    A. G. Baghdasaryan

Preprint series: 03-10, Reports on Analysis

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
46B70 Interpolation between normed linear spaces [See also 46M35]

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

Upload: 2003-08-25

Update: 2003

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