Fractional differentiation for the Gaussian measure and applications

DOI10.1016/j.bulsci.2004.03.009zbMath1108.26007OpenAlexW2057642103MaRDI QIDQ707269

Wilfredo O. Urbina R., Iris Athamaica Lopez Palacios

Publication date: 9 February 2005

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2004.03.009

zbMATH Keywords

Sobolev spacesHermite expansionsFractional derivateFractional integralMeyer's multiplier theoremPotential spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (8)

On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup ⋮ Bessel potential space on the Laguerre hypergroup ⋮ Riesz potentials, Bessel potentials and fractional derivatives on Triebel-Lizorkin spaces for the Gaussian measure ⋮ Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions ⋮ Ornstein–Uhlenbeck operators and semigroups ⋮ Riesz Potentials, Bessel Potentials, and Fractional Derivatives on Besov-Lipschitz Spaces for the Gaussian Measure ⋮ Operators associated with the Jacobi semigroup ⋮ Some results on Gaussian Besov-Lipschitz spaces and Gaussian Triebel-Lizorkin spaces

Cites Work

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• Lectures on stochastic differential equations and Malliavin calculus
• Sobolev spaces of Wiener functionals and Malliavin's calculus
• On the Riesz transforms for Gaussian measures
• Operators associated with the Hermite semigroup - a survey
• On fractional differentiation and integration on spaces of homogeneous type

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