On Riesz transforms and maximal functions in the context of Gaussian Harmonic Analysis

DOI10.1090/S0002-9947-06-04100-6zbMath1128.42006MaRDI QIDQ3420395

Hugo Aimar, Liliana Forzani, Roberto Scotto

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

singular integralsmaximal functionsGaussian measureHermite expansionsFourier analysis in several variables

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) One-parameter semigroups and linear evolution equations (47D06) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Stochastic calculus of variations and the Malliavin calculus (60H07) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items

Higher-order Riesz transforms in the inverse Gaussian setting and UMD Banach spaces, Riesz-Jacobi transforms as principal value integrals, Two-weight norm inequalities for local fractional integrals on Gaussian measure spaces, Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansions, On the maximal operator of a general Ornstein-Uhlenbeck semigroup, The Hardy-Littlewood property and maximal operators associated with the inverse Gauss measure, Weak-type inequality for conjugate first order Riesz-Laguerre transforms, Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator, Some weighted estimates on Gaussian measure spaces, Weighted norm inequalities for local fractional integrals on Gaussian measure spaces, Ornstein–Uhlenbeck operators and semigroups, Riesz transforms for a non-symmetric Ornstein--Uhlenbeck semigroup, Riesz transforms of a general Ornstein-Uhlenbeck semigroup, Variation and oscillation for harmonic operators in the inverse Gaussian setting, The maximal operator of a normal Ornstein-Uhlenbeck semigroup is of weak type (1,1), Local Muckenhoupt weights on Gaussian measure spaces, New Gaussian Riesz transforms on variable Lebesgue spaces

Cites Work

• Higher-order Riesz operators for the Ornstein-Uhlenbeck semigroup
• On the Riesz transforms for Gaussian measures
• Weak-type estimates for the Riesz transform associated with the Gaussian measure
• On higher Riesz transforms for Gaussian measures
• The local part and the strong type for operators related to the Gaussian measure.
• Spectral multipliers for the Ornstein-Uhlenbeck semigroup
• Weak type inequality for a family of singular integral operators related with the Gaussian measure
• A Remark on the Maximal Function for Measures in R n
• Estimates for the Maximal Operator of the Ornstein-Uhlenbeck Semigroup
• Boundedness of Littlewood-Paley g-functions of higher order associated with the Ornstein-Uhlenbeck semigroup
• Hermite Conjugate Expansions
• Some remarks on the multiple Weierstrass transform and Abel summability of multiple Fourier-Hermite series
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
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