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

Eugene B. Fabes; Chritian E. Gutiérrez; Roberto Scotto

Displaying similar documents to “Weak-type estimates for the Riesz transforms associated with the Gaussian measure.”

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.

Riesz transform on manifolds and heat kernel regularity

Pascal Auscher, Thierry Coulhon, Xuan Thinh Duong, Steve Hofmann (2004)

Annales scientifiques de l'École Normale Supérieure

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On conjugate Poisson integrals and Riesz transforms for the Hermite expansions

S. Thangavelu (1993)

Colloquium Mathematicae

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Riesz transform on manifolds and Poincaré inequalitie

Pascal Auscher, Thierry Coulhon (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the validity of the $L^{p}$ inequality for the Riesz transform when $p > 2$ and of its reverse inequality when $1 < p < 2$ on complete riemannian manifolds under the doubling property and some Poincaré inequalities.

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...

Hermite expansions on R for radial functions.

Sundaram Thangavelu (1990)

Revista Matemática Iberoamericana

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Some properties of Holmgren-Riesz transform in two dimensions

M. A. Bassam (1962)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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