On conjugate Poisson integrals and Riesz transforms for the Hermite expansions

S. Thangavelu

Displaying similar documents to “On conjugate Poisson integrals and Riesz transforms for the Hermite expansions”

Weak-type estimates for the Riesz transforms associated with the Gaussian measure.

Eugene B. Fabes, Chritian E. Gutiérrez, Roberto Scotto (1994)

Revista Matemática Iberoamericana

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In this paper we will study the behavior of the Riesz transform associated with the Gaussian measure γ(x)dx = edx in the space L (R).

Riesz means of Fourier transforms and Fourier series on Hardy spaces

Ferenc Weisz (1998)

Studia Mathematica

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Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from $H_{p} (ℝ)$ to $L_{p} (ℝ)$ (1/(α+1) < p < ∞) and is of weak type (1,1), where $H_{p} (ℝ)$ is the classical Hardy space. As a consequence we deduce that the Riesz means of a function $⨍ \in L_{1} (ℝ)$ converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on $H_{p} (ℝ)$ whenever 1/(α+1) < p < ∞. Thus, in case $⨍ \in H_{p} (ℝ)$ , the Riesz...

The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)

Liliana Forzani, Roberto Scotto (1998)

Studia Mathematica

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The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator $L : = d^{2} / d x^{2} - 2 x d / d x$ , x ∈ ℝ, need not be of weak type (1,1). A function in $L^{1} (d γ)$ , where dγ is the Gaussian measure, is given such that the distribution function of the higher order Riesz transform decays more slowly than C/λ.

Hermite expansions on R for radial functions.

Sundaram Thangavelu (1990)

Revista Matemática Iberoamericana

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Multipliers for Hermite expansions.

Sundaram Thangavelu (1987)

Revista Matemática Iberoamericana

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The aim of this paper is to prove certain multiplier theorems for the Hermite series.

On Limiting Case of the Stein-Weiss Type Inequality for the B-Riesz Potentials

Guliyev, Emin (2009)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: Primary 42B20, 42B25, 42B35 In this paper we study the Riesz potentials (B-Riesz potentials) generated by the Laplace-Bessel differential operator ∆B [...]. We establish an inequality of Stein-Weiss type for the B-Riesz potentials in the limiting case, and obtain the boundedness of the B-Riesz potential operator from the space Lp,|x|β,γ to BMO|x|−λ,γ. * Emin Guliyev’s research partially supported by the grant of INTAS YS Collaborative...

Some remarks on Bochner-Riesz means

S. Thangavelu (2000)

Colloquium Mathematicae

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We study $L^{p}$ norm convergence of Bochner-Riesz means $S_{R}^{δ} f$ associated with certain non-negative differential operators. When the kernel $S_{R}^{m} (x, y)$ satisfies a weak estimate for large values of m we prove $L^{p}$ norm convergence of $S_{R}^{δ} f$ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.

On almost everywhere and mean convergence of Hermite and Laguerre expansions

S. Thangavelu (1990)

Colloquium Mathematicae

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A simple proof of the $L^{p}$ continuity of the higher order Riesz transforms with respect to the gaussian measure $γ_{d}$

Liliana Forzani, Roberto Scotto, Wilfredo Urbina (2001)

Séminaire de probabilités de Strasbourg

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On A Mercerian Theorem And It's Application To The Equiconvergence Of Cesàro And Riesz Transforms

Shimshon Zimering (1961)

Publications de l'Institut Mathématique

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Remark On Fatou-Riesz's Theorem

Vojislav G. Avakumović (1955)

Publications de l'Institut Mathématique

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