Multivariate spectral multipliers for systems of Ornstein–Uhlenbeck operators
Tom 216 / 2013
Studia Mathematica 216 (2013), 47-67
MSC: Primary 42B15; Secondary 42C10; Tertiary 47A60.
DOI: 10.4064/sm216-1-4
Streszczenie
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.
