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arXiv · 1207.4217

Rs-sectorial operators and generalized Triebel-Lizorkin spaces

Peer Christian Kunstmann·Alexander Ullmann
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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.

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Peer Christian Kunstmann, Alexander Ullmann. 2012-07-17. Rs-sectorial operators and generalized Triebel-Lizorkin spaces. https://arxiv.org/abs/1207.4217

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