**
J. Rákosník (ed.), **

Function spaces, differential operators and nonlinear analysis.

Proceedings of the conference held in Paseky na Jizerou, September 3-9, 1995.

Mathematical Institute, Czech Academy of Sciences, and Prometheus Publishing House, Praha 1996

p. 267 - 272

#
Function spaces of Lizorkin-Triebel type with exponential weights

##
Thomas Schott

Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, Leutragraben 1, 07743 Jena, Germany schott@minet.uni-jena.de

**Abstract:** This talk deals with weighted function spaces of the type $F^s_{pq}(u)$ on the Euclidean space $\Bbb R^n$, where $1<p<\infty, 1<q\leq\infty$ and $s\in \Bbb R$. Spaces of type $F^s_{pq}$ generalize the fractional Sobolev spaces $H^s_p$ with the classical Sobolev spaces $W^s_p$ as a subclass. The weight functions $u$ are of at most exponential growth. In particular, $u(x)=\exp(\pm|x|)$ is an admissible weight function. We study a suitable space of distributions and give some basic properties of the spaces $F^s_{pq}(u)$. Furthermore, we prove that $F^s_{p2}(u)=W^s_p(u), s\in\Bbb N_0$, where $W^s_p(u)$ are weighted Sobolev spaces.

**Full text of the article:**

[Previous Article] [Next Article] [Table of Contents]