---
res:
  bibo_abstract:
  - 'Let (E, H, μ) be an abstract Wiener space and let DV : = V D, where D denotes
    the Malliavin derivative and V is a closed and densely defined operator from H
    into another Hilbert space under(H, {combining low line}). Given a bounded operator
    B on under(H, {combining low line}), coercive on the range over(R (V), -), we
    consider the operators A : = V* B V in H and under(A, {combining low line}) :
    = V V* B in under(H, {combining low line}), as well as the realisations of the
    operators L : = DV* B DV and under(L, {combining low line}) : = DV DV* B in Lp
    (E, μ) and Lp (E, μ ; under(H, {combining low line})) respectively, where 1 <
    p < ∞. Our main result asserts that the following four assertions are equivalent:
    (1)D (sqrt(L)) = D (DV) with {norm of matrix} sqrt(L) f {norm of matrix}p {minus
    tilde} {norm of matrix} DV f {norm of matrix}p for f ∈ D (sqrt(L));(2)under(L,
    {combining low line}) admits a bounded H∞-functional calculus on over(R (DV),
    -);(3)D (sqrt(A)) = D (V) with {norm of matrix} sqrt(A) h {norm of matrix} {minus
    tilde} {norm of matrix} V h {norm of matrix} for h ∈ D (sqrt(A));(4)under(A, {combining
    low line}) admits a bounded H∞-functional calculus on over(R (V), -). Moreover,
    if these conditions are satisfied, then D (L) = D (DV2) ∩ D (DA). The equivalence
    (1)-(4) is a non-symmetric generalisation of the classical Meyer inequalities
    of Malliavin calculus (where under(H, {combining low line}) = H, V = I, B = frac(1,
    2) I). A one-sided version of (1)-(4), giving Lp-boundedness of the Riesz transform
    DV / sqrt(L) in terms of a square function estimate, is also obtained. As an application
    let -A generate an analytic C0-contraction semigroup on a Hilbert space H and
    let -L be the Lp-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. The boundedness of the Riesz transform
    is used to obtain an Lp-domain characterisation for the operator L.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Jan
      foaf_name: Jan Maas
      foaf_surname: Maas
      foaf_workInfoHomepage: http://www.librecat.org/personId=4C5696CE-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-0845-1338
  - foaf_Person:
      foaf_givenName: Jan
      foaf_name: van Neerven, Jan M
      foaf_surname: Van Neerven
  bibo_doi: 10.1016/j.jfa.2009.07.001
  bibo_issue: '8'
  bibo_volume: 257
  dct_date: 2009^xs_gYear
  dct_publisher: Academic Press@
  dct_title: Boundedness of Riesz transforms for elliptic operators on abstract Wiener
    spaces@
...