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arXiv · 1407.0821

Paley-Littlewood decomposition for sectorial operators and interpolation spaces

Christoph Kriegler·Lutz Weis
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Abstract

We prove Paley-Littlewood decompositions for the scales of fractional powers of $0$-sectorial operators $A$ on a Banach space which correspond to Triebel-Lizorkin spaces and the scale of Besov spaces if $A$ is the classical Laplace operator on $L^p(\mathbb{R}^n).$We use the $H^\infty$-calculus, spectral multiplier theorems and generalized square functions on Banach spaces and apply our results to Laplace-type operators on manifolds and graphs, Schrödinger operators and Hermite expansion.We also give variants of these results for bisectorial operators and for generators of groups with a bounded $H^\infty$-calculus on strips.

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Christoph Kriegler, Lutz Weis. 2016-02-19. Paley-Littlewood decomposition for sectorial operators and interpolation spaces. https://doi.org/10.1002/mana.201400223

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