This is an announcement for the paper "Rs-sectorial operators and generalized Triebel-Lizorkin spaces" by Peer Christian Kunstmann and Alexander Ullmann.

Abstract: We introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of $\mathcal{R}_s$-sectorial operators, which in turn is based on the notion of $\mathcal{R}_s$-bounded sets of operators introduced by Lutz Weis, we obtain a neat theory including equivalence of various norms and a precise description of real and complex interpolation spaces. Another main result of this article is that an $\mathcal{R}_s$-sectorial operator always has a bounded $H^\infty$-functional calculus in its associated generalized Triebel-Lizorkin spaces.

Archive classification: math.FA

Mathematics Subject Classification: 46E30, 47A60, 47B38 (Primary), 42B25 (Secondary)

Remarks: 44 pages

Submitted from: alexander.ullmann@gmx.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.4217

or

http://arXiv.org/abs/1207.4217