| Abstract: | We obtain a general Marcinkiewicz-type multiplier theorem for mixed systems of strongly commuting operators (L=(L_1,ldots ,L_d);) where some of the operators in L have only a holomorphic functional calculus, while others have additionally a Marcinkiewicz-type functional calculus. Moreover, we prove that specific Laplace transform type multipliers of the pair ((mathcal {L},A)) are of certain weak type (1, 1). Here (mathcal {L}) is the Ornstein-Uhlenbeck operator while A is a non-negative operator having Gaussian bounds for its heat kernel. Our results include the Riesz transforms (A(mathcal {L}+A)^{-1},) (mathcal {L}(mathcal {L}+A)^{-1}). |
