  Let (E,H,mu) be an abstract Wiener space and let D_V := VD, where D denotes
the Malliavin derivative and V is a closed and densely defined operator from H
into another Hilbert space G. Given a bounded operator B on G, coercive on the
closure of the range of V, we consider the realisation of the operator D_V* B
D_V in L^p(E,mu) for 1<p<\infty. Our main result states that the following
assertions are equivalent:
  (1) dom((sqrt(D_V* B D_V)) = dom(D_V) and Meyer's inequalities hold for D_V*
B D_V;
  (2) D_V D_V* B admits a bounded H-infinity calculus on the closure of the
range of D_V;
  (3) dom(sqrt(V*BV)) = dom(V) and Meyer's inequalities hold for V*BV;
  (4) VV*B admits a bounded H-infinity calculus on the closure of the range of
V.
  Moreover, if these conditions are satisfied, then dom(L) = dom(D_V^2) \cap
dom(D_A). The equivalence of (1)-(4) is a non-symmetric generalisation of the
classical Meyer inequalities (which correspond to the case G=H, V=I, B=I). A
one-sided version of the main result, giving L^p-boundedness of the associated
Riesz transforms in terms of a square function estimate, is also obtained.
  As an application let -A generate an analytic C_0-contraction semigroup on a
Hilbert space H and let -L be the L^p-realisation of the generator of its
second quantisation. Our results imply that two-sided bounds for the Riesz
transform of L are equivalent with the Kato square root property for A.
