On higher Riesz transforms for Gaussian measures

DOI10.1007/s00041-001-4044-1zbMath0893.42007OpenAlexW2021301490MaRDI QIDQ1357298

Carlos Segovia, José Luis Torrea, Cristian E. Gutiérrez

Publication date: 19 July 1998

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-001-4044-1

zbMATH Keywords

eigenvaluesHermite polynomialsvector-valued inequalitieshigher Riesz transformsLittlewood-Paley-Stein theory of square functionssecond-order partial differential operators

Mathematics Subject Classification ID

Gaussian processes (60G15) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Estimates of eigenvalues in context of PDEs (35P15) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Chaotic behavior of the Riesz transforms for Hermite expansions ⋮ Operators associated with the Hermite semigroup - a survey ⋮ Maximal operators, Littlewood-Paley functions and variation operators associated with nonsymmetric Ornstein-Uhlenbeck operators ⋮ The Hardy-Littlewood property and maximal operators associated with the inverse Gauss measure ⋮ A counterexample to \(L^{\infty}\)-gradient type estimates for Ornstein-Uhlenbeck operators ⋮ Weak-type inequality for conjugate first order Riesz-Laguerre transforms ⋮ Linear combinations of composition operators on the Fock-Sobolev spaces ⋮ Morrey-type spaces on Gauss measure spaces and boundedness of singular integrals ⋮ Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator ⋮ Fractional maximal operator on Musielak-Orlicz spaces over unbounded quasi-metric measure spaces ⋮ BMO and \(H^{1}\) for the Ornstein-Uhlenbeck operator ⋮ Fock-Sobolev spaces of fractional order ⋮ Higher order Riesz transforms associated with Bessel operators ⋮ A maximal function characterization of the Hardy space for the Gauss measure ⋮ Pointwise multipliers for Campanato spaces on Gauss measure spaces ⋮ Comparison of spaces of Hardy type for the Ornstein-Uhlenbeck operator ⋮ Generalized Ornstein-Uhlenbeck semigroups: Littlewood-Paley-Stein inequalities and the P. A. Meyer equivalence of norms ⋮ $L^p $ boundedness of Riesz transforms for orthogonal polynomials in a general context ⋮ Ornstein–Uhlenbeck operators and semigroups ⋮ ON THE DOMAIN OF NONSYMMETRIC ORNSTEIN–UHLENBECK OPERATORS IN BANACH SPACES ⋮ Riesz transforms for a non-symmetric Ornstein--Uhlenbeck semigroup ⋮ Riesz transforms of a general Ornstein-Uhlenbeck semigroup ⋮ Spectral multipliers for the Ornstein-Uhlenbeck semigroup ⋮ On Riesz transforms and maximal functions in the context of Gaussian Harmonic Analysis ⋮ Riesz transforms on variable Lebesgue spaces with Gaussian measure ⋮ The local part and the strong type for operators related to the Gaussian measure. ⋮ New Gaussian Riesz transforms on variable Lebesgue spaces

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