Riesz potentials, Bessel potentials and fractional derivatives on Triebel-Lizorkin spaces for the Gaussian measure

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:422

Article

Gatto, A. Eduardo¹  Pineda, Ebner²  Urbina, Wilfredo O.³ 

[1] Depaul Univ, Dept Math Sci, Chicago, IL 60614 USA

[2] UCLA, Dept Matemat, Barquisimeto 3001, Venezuela

[3] Roosevelt Univ, Dept Math & Actuarial Sci, Chicago, IL 60605 USA

关键词: Hermite expansions;    Fractional integration;    Fractional differentiation;    Triebel-Lizorkin spaces;    Gaussian measure;   

DOI  :  10.1016/j.jmaa.2014.08.022

来源: Elsevier

【 摘 要 】

In [3] the boundedness properties of Riesz potentials, Bessel potentials and fractional derivatives were studied in detail on Gaussian Besov-Lipschitz spaces B-p,q(alpha)(gamma(d)). In this paper we will continue our study proving the boundedness of those operators on Gaussian Triebel-Lizorkin spaces F-p,q(alpha)(gamma(d)). Also, these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free