Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators
Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators are studied. We prove that -uniform, 1 < p < ∞, spectral multipliers extend to holomorphic functions in some subset of a polysector, depending on p. We also characterize L¹-uniform spectral multipliers and prove a Marcinkiewicz-type multiplier theorem. In the appendix we obtain analogous results for systems of Laguerre operators.