# Claudio Pita Ruiz

## Log-Sobolev and related inequalities in mu-deformed Segal-Bargmann spaces

We consider a generalization (a mu-deformation) of the Segal-Bargmann transform. We study this generalization as an operator between L^p spaces and then we obtain sufficient conditions for this operator to be bounded. A family of Hirschman type inequalities involving the Shannon entropies of a function and of its generalized Segal-Bargmann transform are proved. We also prove a parametrized family of log-Sobolev inequalities, in which a new quantity that we call "dilation energy" appears. This quantity generalizes the "energy term" that has appeared in previous works.