Logarithmic Sobolev inequalities: Regularizing effect of Levy operators and asymptotic convergence in the Levy-Fokker-Planck equation.

In this paper we study some applications of the Levy logarithmic Sobolev inequality to the study of the regularity of the solution of the fractal heat equation, i.e. the heat equation where the Laplacian is replaced with the fractional Laplacian. It is also used to the study of the asymptotic behaviour of the Levy-Ornstein-Uhlenbeck process. [ABSTRACT FROM AUTHOR]