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Título: | Singular integrals in quantum Euclidean spaces |
Autor: | González-Pérez, Adrián M.; Junge, Marius; Parcet, Javier CSIC ORCID | Fecha de publicación: | 2021 | Editor: | American Mathematical Society | Citación: | MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY 272: 1- 87 (2021) | Resumen: | In this paper, we establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes¿ pseudodifferential calculus for rotation algebras, thanks to a new form of Calder¿on-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce Lp-boundedness and Sobolev p-estimates for regular, exotic and forbidden symbols in the expected ranks. In the L2 level both Calder¿on-Vaillancourt and Bourdaud theorems for exotic and forbidden symbols are also generalized to the quantum setting. As a basic application of our methods, we prove Lp-regularity of solutions for elliptic PDEs | Versión del editor: | http://dx.doi.org/10.1090/memo/1334 | URI: | http://hdl.handle.net/10261/253748 | DOI: | 10.1090/memo/1334 | Identificadores: | doi: 10.1090/memo/1334 issn: 0065-9266 |
Aparece en las colecciones: | (ICMAT) Artículos |
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preprint_parcet@icmat.es_021121-074057.pdf | 783,75 kB | Adobe PDF | Visualizar/Abrir |
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