Log-Sobolev inequalities for semi-direct product operators and   applications
  We prove logarithmic Sobolev inequalities for semi-direct product operators (see definition in Section 1). We apply our main results to examples of operators and provide some applications to ultracontractive bounds of semigroups. Hardy's inequalities are proved and use to study some operators of Grushin's type. 
Piero D'Ancona, Patrick Maheux (MAPMO), Vittoria Pierfelice (MAPMO)
math.AP math.FA