Extended Sobolev Scale and Elliptic Operators

  • V. A. Mikhailets
  • A. A. Murach


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