Algebraic Calderón-Zygmund theory

Autor: Tao Mei, Runlian Xia, Marius Junge, Javier Parcet
Přispěvatelé: Ministerio de Economía y Competitividad (España), European Commission
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Digital.CSIC. Repositorio Institucional del CSIC
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ISSN: 0001-8708
Popis: Calder´on-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov semigroup satisfying purely algebraic assumptions. We shall construct an abstract form of ‘Markov metric’ governing the Markov process and the naturally associated BMO spaces, which interpolate with the Lp-scale and admit endpoint inequalities for Calder´on-Zygmund operators. Motivated by noncommutative harmonic analysis, this approach gives the first form of Calder´on-Zygmund theory for arbitrary von Neumann algebras, but is also valid in classical settings like Riemannian manifolds with nonnegative Ricci curvature or doubling/nondoubling spaces. Other less standard commutative scenarios like fractals or abstract probability spaces are also included. Among our applications in the noncommutative setting, we improve recent results for quantum Euclidean spaces and group von Neumann algebras, respectively linked to noncommutative geometry and geometric group theory.
Mei is partially supported by NSF grant DMS1700171. Javier Parcet is supported by the Europa Excelencia Grant MTM2016-81700-ERC and the CSIC Grant PIE-201650E030. Javier Parcet and Runlian Xia are supported by ICMAT Severo Ochoa Grant SEV-2015-0554 (Spain).
Databáze: OpenAIRE
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