2017
Том 69
№ 9

All Issues

Extended Sobolev Scale and Elliptic Operators

Mikhailets V. A., Murach A. A.

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Abstract

We obtain a constructive description of all Hilbert function spaces that are interpolation spaces with respect to a couple of Sobolev spaces $[H^{(s_0)}(\mathbb{R}^n), H^{(s_1)}(\mathbb{R}^n)]$ of some integer orders $s_0$ and $s_1$ and that form an extended Sobolev scale. We find equivalent definitions of these spaces with the use of uniformly elliptic pseudodifferential operators positive definite in $L_2(\mathbb{R}^n)$. Possible applications of the introduced scale of spaces are indicated.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 3, pp 435-447.

Citation Example: Mikhailets V. A., Murach A. A. Extended Sobolev Scale and Elliptic Operators // Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 392-404.

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