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

Liliana Forzani; Roberto Scotto — 1998

Studia Mathematica

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.

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

$L^{p}$ boundedness of Riesz transforms for orthogonal polynomials in a general context

Liliana Forzani; Emanuela Sasso; Roberto Scotto — 2015

Studia Mathematica

Nowak and Stempak (2006) proposed a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal expansions, and proved their boundedness on L². Following them, we give easy to check sufficient conditions for their boundedness on $L^{p}$ , 1 < p < ∞. We also discuss the symmetrized version of these transforms.

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

Eugene B. Fabes; Chritian E. Gutiérrez; Roberto Scotto — 1994

Revista Matemática Iberoamericana

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).

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Currently displaying 1 – 4 of 4

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

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

$L^{p}$ boundedness of Riesz transforms for orthogonal polynomials in a general context

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

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Formula preview

Currently displaying 1 – 4 of 4

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

A simple proof of the L p continuity of the higher order Riesz transforms with respect to the gaussian measure γ d

L p boundedness of Riesz transforms for orthogonal polynomials in a general context

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

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

$L^{p}$ boundedness of Riesz transforms for orthogonal polynomials in a general context