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Title

Singular integrals in quantum Euclidean spaces

AuthorsGonzález-Pérez, Adrián M. ; Junge, Marius ;Parcet, Javier
Issue Date2021
PublisherAmerican Mathematical Society
CitationMEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY 272: 1- 87 (2021)
AbstractIn 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
Publisher version (URL)http://dx.doi.org/10.1090/memo/1334
URIhttp://hdl.handle.net/10261/253748
Identifiersdoi: 10.1090/memo/1334
issn: 0065-9266
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