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Resumen de Instanteneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations

Julia Matos, Philippe Souplet Árbol académico

  • 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.

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