Let (E,H,μ) be an abstract Wiener space and let DV :=VD, where D denotes the Malliavin derivative
and V is a closed and densely defined operator from H into another Hilbert space H. Given a bounded
operator B on H, coercive on the range R(V ), we consider the operators A := V ∗BV in H and A := VV∗B
in H, as well as the realisations of the operators L := D∗V BDV and L := DV D∗V B in Lp(E,μ) and
Lp(E,μ;H) respectively, where 1
Keywords :
H?-functional calculus , R-boundedness , Divergence form elliptic operators , Hodge decomposition , Abstract Wiener spaces , Domain characterisationin Lp , Kato square root problem , Ornstein–Uhlenbeck operator , Second quantised operators , Meyer inequalities , Hodge–Dirac operators , Square function estimates , Riesz transforms