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

JOURNAL OF APPROXIMATION THEORY

卷:161

Article

Pineda, Ebner²  Urbina, Wilfredo^1,3 

[1] UCV, Dept Matemat, Fac Ciencias, Caracas 1041, Venezuela

[2] Univ Calif Los Angeles, Dept Matemat Decanato Ciencia & Tecnol, Barquisimeto 3001, Venezuela

[3] De Paul Univ, Dept Math Sci, Chicago, IL 60614 USA

关键词: Hermite expansions;    Fractional integrals;    Fractional derivatives;    Bessel potentials;    Triebel-Lizorkin spaces;    Besov-Lipschitz spaces;   

DOI  :  10.1016/j.jat.2008.11.010

来源: Elsevier

【 摘 要 】

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-alpha(p)(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 diffusion semigroups. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free