Geodesic
Multivariate spectral multipliers for systems of Ornstein–Uhlenbeck operators
Błażej Wróbel1
1 Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Studia Mathematica, Tome 216 (2013) no. 1, pp. 47-67 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Multivariate spectral multipliers for systems of Ornstein–Uhlenbeck operators are studied. We prove that $L^p$-uniform, $1 p \infty ,$ spectral multipliers extend to holomorphic functions in some subset of a polysector, depending on $p.$ We also characterize $L^1$-uniform spectral multipliers and prove a Marcinkiewicz-type multiplier theorem. In the appendix we obtain analogous results for systems of Laguerre operators.
DOI : 10.4064/sm216-1-4
Keywords: multivariate spectral multipliers systems ornstein uhlenbeck operators studied prove p uniform infty spectral multipliers extend holomorphic functions subset polysector depending characterize uniform spectral multipliers prove marcinkiewicz type multiplier theorem appendix obtain analogous results systems laguerre operators

Błażej Wróbel 1

1 Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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Błażej Wróbel. Multivariate spectral multipliers for
 systems of Ornstein–Uhlenbeck operators. Studia Mathematica, Tome 216 (2013) no. 1, pp. 47-67. doi: 10.4064/sm216-1-4

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