Resumen de Instanteneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations
We consider the Hermite semigroup, generated by the operator ?-¿y.? in RN.
We establish instantaneous smoothing estimates for the Hermite semigroup in the uniformly local Lebesgue spaces introduced by Kato [1].
It was known from the classical works of Nelson [3] and Gross [2] that such smooting properties fail in usual weighted Lebesgue spaces. This linear result enables us to prove instantaneous smoothing estimates for some related nonlinear parabolic problems.
