A characterization of the Gaussian Lipschitz space and sharp estimates for the Ornstein-Uhlenbeck Poisson kernel

DOI10.4171/RMI/912zbMath1372.46028arXiv1401.4288OpenAlexW2964007868MaRDI QIDQ515344

Peter Sjögren, Li Guang Liu

Publication date: 13 March 2017

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.4288

zbMATH Keywords

Lipschitz spaceGaussian measure spaceOrnstein-Uhlenbeck Poisson kernel

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Lipschitz (Hölder) classes (26A16) Groups and semigroups of linear operators (47D03) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (8)

A Calderón theorem for the Poisson semigroups associated with the Ornstein-Uhlenbeck and Hermite operators ⋮ A new characterization of the Besov spaces associated with Hermite operator ⋮ Regularity property of some operators on Lipschitz spaces and homogeneous Lipschitz spaces associated with biharmonic operator ⋮ Parabolic Hermite Lipschitz spaces: regularity of fractional operators ⋮ Ornstein–Uhlenbeck operators and semigroups ⋮ Pointwise convergence to initial data of heat and Laplace equations ⋮ Lipschitz spaces adapted to Schrödinger operators and regularity properties ⋮ Discrete Hölder spaces and their characterization via semigroups associated with the discrete Laplacian and kernel estimates

Cites Work

• Unnamed Item
• Some results on Gaussian Besov-Lipschitz spaces and Gaussian Triebel-Lizorkin spaces
• Pointwise convergence to initial data of heat and Laplace equations
• Riesz Potentials, Bessel Potentials, and Fractional Derivatives on Besov-Lipschitz Spaces for the Gaussian Measure
• On Gaussian Lipschitz spaces and the boundedness of fractional integrals and fractional derivatives on them
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)

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