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Norm-generating pseudodifferential operators in the spaces $$W_p^s (\mathbb{R}^n)$$. (English. Russian original) Zbl 1006.46025
Function spaces, harmonic analysis, and differential equations. Collected papers. Dedicated to the 95th anniversary of academician S. M. Nikol’skii. Transl. from the Russian. Moscow: MAIK Nauka/Interperiodika Publishing, Proc. Steklov Inst. Math. 232, 52-65 (2001); translation from Tr. Mat. Inst. Steklova 232, 58-71 (2001).
Let $$s\geq 0$$, $$1<p< \infty$$, $$\frac{1}{p} + \frac{1}{p'} =1$$. Let $$W^s_p ({\mathbb R}^n)$$ be the well-known Sobolev-Slobodeckij spaces. A mapping $$A$$ from $$W^s_p ({\mathbb R}^n)$$ into its dual $$W^{-s}_{p'} ({\mathbb R}^n)$$ is called norm-generating if $(Au,u) = \|Au |W^{-s}_{p'} ({\mathbb R}^n) \|\cdot \|u |W^s_p ({\mathbb R}^n) \|, \quad u \in W^s_p ({\mathbb R}^n).$ It is the aim of this paper to study the structure of these operators $$A$$.
For the entire collection see [Zbl 0981.00017].
##### MSC:
 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47G30 Pseudodifferential operators
##### Keywords:
Sobolev-Slobodeckij spaces; norm-generating map