Extended Sobolev Scale and Elliptic Operators

  • V. A. Mikhailets
  • A. A. Murach

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.
Published
25.03.2013
How to Cite
MikhailetsV. A., and MurachA. A. “Extended Sobolev Scale and Elliptic Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 3, Mar. 2013, pp. 392-04, http://umj.imath.kiev.ua/index.php/umj/article/view/2426.
Section
Research articles