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Riesz transforms on generalized Heisenberg groups and Riesz transforms associated to the CCR heat flow
Lust-Piquard, Françoise

Data: 2004
Resum: Let 1 < q < [infinity]. We prove that the Riesz transforms Rk = XkL-1/2 on a generalized Heisenberg group G satisfy [fòrmula matemàtica] where K, J are respectively the dimensions of the first and second layer of the Lie algebra of G. We prove similar inequalities on Schatten spaces Sq(H), with dimension free constants, for Riesz transforms associated to commuting inner *-derivation Dk and a suitable substitute of the square function. An example is given by the derivations associated to n commuting pairs of operators (Pj, Qj) on a Hilbert space H satisfying the canonical commutation relations [Pj, Qj] = iIH.
Drets: Tots els drets reservats.
Llengua: Castellà.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Heat operator ; Riesz transforms ; H-groups ; Commuting *-inner derivations
Publicat a: Publicacions matematiques, V. 48 N. 2 (2004) , p. 309-333, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_48204_02

26 p, 218.1 KB

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