Some results on Gaussian Besov-Lipschitz spaces and Gaussian Triebel-Lizorkin spaces

In this paper we define Besov-Lipschitz and Triebel-Lizorkin spaces in the context of Gaussian harmonic analysis, the harmonic analysis of Hermite polynomial expansions. We study inclusion relations among them, some interpolation results and continuity results of some important operators (the Ornstein-Uhlenbeck and the Poisson-Hermite semigroups and the Bessel potentials) on them. We also prove that the Gaussian Sobolev spaces $L^p_\alpha(\gamma_d)$ are contained in them. The proofs are general enough to allow extensions of these results to the case of Laguerre or Jacobi expansions and even further in the general framework of diffusions semigroups

Operador de superposición uniformemente acotado en espacios de funciones de segunda variación acotada en el sentido de Shiba

In this paper we introduce the notion of “function of second bounded variation” in the sense of Shiba, and we show that if a superposition operator applies the space of all such functions on itself and it is uniformly bounded, then its generating function satisfies a Matkowski condition.  En este trabajo introducimos la noción de función de segunda variación acotada en el sentido de Shiba y mostramos que si un operador de superposición aplica el espacio de todas estas funciones en sí mismo y es uniformemente acotado, entonces su función generadora satisface una condición de Matkowski