Gaussian Harmonic Analysis

DOI10.1007/978-3-030-05597-4zbMath1421.42001OpenAlexW2951107997MaRDI QIDQ4645335

Wilfredo O. Urbina R.

Publication date: 10 January 2019

Published in: Springer Monographs in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-05597-4

zbMATH Keywords

maximal functionsingular integralharmonic analysisHermite polynomialsOrnstein-Uhlenbeck operatorGaussian measurefunction spaceshypercontractivityspectral multiplier operatorsOrnstein-Uhlenbeck semigroupPoisson-Hermite semigroup

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) One-parameter semigroups and linear evolution equations (47D06) Multipliers for harmonic analysis in several variables (42B15) Markov semigroups and applications to diffusion processes (47D07) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Stochastic calculus of variations and the Malliavin calculus (60H07) (H^p)-spaces (42B30) Conjugate functions, conjugate series, singular integrals (42A50) Polynomials, rational functions in real analysis (26C99) Nontrigonometric harmonic analysis (42C99) Harmonic analysis in one variable (42A99) Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces (42-02)

Related Items (23)

Chebyshev--Hermite Polynomials and Distributions of Polynomials in Gaussian Random Variables ⋮ Integral operators on Fock-Sobolev spaces via multipliers on Gauss-Sobolev spaces ⋮ Two-weight norm inequalities for local fractional integrals on Gaussian measure spaces ⋮ On the maximal operator of a general Ornstein-Uhlenbeck semigroup ⋮ Reduction principle for Gaussian \(K\)-inequality ⋮ A Calderón theorem for the Poisson semigroups associated with the Ornstein-Uhlenbeck and Hermite operators ⋮ Restriction theorem fails for the Fourier-Hermite transform associated with the normalized Hermite polynomials with respect to a discrete surface ⋮ Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting ⋮ The Hardy-Littlewood property and maximal operators associated with the inverse Gauss measure ⋮ An extension problem, trace Hardy and Hardy's inequalities for the Ornstein-Uhlenbeck operator ⋮ On the \(L^2\) boundedness of pseudo-multipliers for Hermite expansions ⋮ On some operators associated with non-degenerate symmetric \(\alpha \)-stable probability measures ⋮ Sobolev and Besov classes on infinite-dimensional spaces ⋮ Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator ⋮ Sharp exponential inequalities for the Ornstein-Uhlenbeck operator ⋮ Fock space on \(\mathbb{C}^\infty\) and Bose-Fock space ⋮ Some weighted estimates on Gaussian measure spaces ⋮ Discrete-continuous Jacobi-Sobolev spaces and Fourier series ⋮ Riesz transforms of a general Ornstein-Uhlenbeck semigroup ⋮ Optimal angle of the holomorphic functional calculus for the Ornstein-Uhlenbeck operator ⋮ New Brezis-van Schaftingen-Yung-Sobolev type inequalities connected with maximal inequalities and one parameter families of operators ⋮ New Gaussian Riesz transforms on variable Lebesgue spaces ⋮ Boundedness of the Maximal Function of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure and consequences

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