Fractional differentiation for the Gaussian measure and applications
type: Item
instance of: scholarly article
title: Fractional differentiation for the Gaussian measure and applications
zbMATH Open document ID: 1108.26007
published in: Bulletin des Sciences Mathématiques
publication date: 2005-02-09T00:00:00Z
review text: The authors define the fractional derivative of order \(\alpha\) such that \(0<\alpha< 1\), associated with respect to Gaussian measure. Characterization of the Gaussian potential spaces is obtained in terms of the fractional derivative operators, defined in this paper, to study the relation between potential spaces \(L^p_k(\gamma_1)\) and Sobolev spaces \(W^p_k(\gamma_1)\). Indeed, the authors have extensively written the section of introduction by presenting all possible terminologies and various definitions. The analyses, employed in proving the theorems, are explicit and comprehensive. The paper concludes by obtaining Calderon's reproduction formula for the Gaussian measure in terms of this fractional derivative.
reviewed by: P. K. Banerji
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 2132860
zbMATH Keywords: Hermite expansions
zbMATH Keywords: Fractional integral
zbMATH Keywords: Fractional derivate
zbMATH Keywords: Potential spaces
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Meyer's multiplier theorem
author: Iris Athamaica Lopez Palacios
author: Wilfredo O. Urbina
MaRDI profile type: Publication
full work available at URL: j.bulsci.2004.03.009
OpenAlex ID: W2057642103
cites work: On fractional differentiation and integration on spaces of homogeneous type
cites work: On the Riesz transforms for Gaussian measures
cites work: Q3332040
cites work: Operators associated with the Hermite semigroup - a survey
cites work: Q5607484
cites work: Sobolev spaces of Wiener functionals and Malliavin's calculus
cites work: Q3971012
cites work: Lectures on stochastic differential equations and Malliavin calculus
DOI: 10.1016/J.BULSCI.2004.03.009
description: scientific article; zbMATH DE number 2132860