On Hirschman and log-Sobolev inequalities in mu-deformed Segal-Bargmann   analysis
  We consider a deformation of Segal-Bargmann space and its transform. We study L^p properties of this transform and obtain entropy-entropy inequalities (Hirschman) and entropy-energy inequalities (log-Sobolev) that generalize the corresponding known results in the undeformed theory. 
C. Pita-Ruiz, S.B. Sontz