Boundedness of Riesz transforms for elliptic operatorson abstract Wiener spaces

摘要

Let (E, H, μ) be an abstract Wiener space and let Dv:= V D, where D denotes the Malliavin derivativeand V is a closed and densely defined operator from H into another Hilbert space H. Given a boundedoperator B on H, coercive on the range R(V), we consider the operators A := V~* BVinHand A :=V V~* Bin H, as well as the realisations of the operators L := D_V~*,BD_VandL :=D_V V~* BinL~p (E , μ)andL~p (E,μ; H)respectively, where 1 <∞.Our main result asserts that the following four assertions areequivalent.