J. Rákosník (ed.),
Function spaces, differential operators and nonlinear analysis.
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.

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