Paley-Littlewood decomposition for sectorial operators and interpolation spaces

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• 作者：Christoph Kriegler and Lutz Weis
• 刊名：Mathematische Nachrichten
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：289
• 期：11-12
• 页码：1488-1525
• 全文大小：537K
• ISSN：1522-2616

文摘

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 www.w3.org/1998/Math/MathML">w xmlns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">Lpw>(Rn)w>.w> We use the www.w3.org/1998/Math/MathML">w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">H∞-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 www.w3.org/1998/Math/MathML">w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">H∞-calculus on strips.