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On spaces of functions of variable smoothness defined by pseudodifferential operators. (English. Russian original) Zbl 0978.46018
Proc. Steklov Inst. Math. 227, 50-69 (1999); translation from Tr. Mat. Inst. Steklova 227, 56-74 (1999).
Let $$B^{s,a}_{p,q} ({\mathbb R}^n)$$ be spaces of Besov type, where $$1 \leq p \leq \infty$$, $$1 \leq q \leq \infty$$, $$s > 0$$, have the usual meaning and $$a$$ stands for the symbol of a related pseudodifferential operator. These spaces have been introduced by H.-G. Leopold. It is the aim of this paper to study new equivalent norms in terms of differences and to prove real and complex interpolation theorems.
For the entire collection see [Zbl 0952.00006].

##### MSC:
 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46B70 Interpolation between normed linear spaces 35S05 Pseudodifferential operators as generalizations of partial differential operators