M. Fuhrman, HYPERCONTRACTIVITY OF NONSYMMETRIC ORNSTE IN-UHLENBECK SEMIGROUPS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 321(7), 1995, pp. 929-932
We prove hypercontractivity of some nonsymmetric Ornstein-Uhlenbeck se
migroups in Hilbert spaces. In our setting logarithmic Sobolev inequal
ities do not hold in general.