Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

Adam Nowak; Luz Roncal; Krzysztof Stempak

Displaying similar documents to “Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator”

Riesz spaces of order bounded disjointness preserving operators

Fethi Ben Amor (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let $L$ , $M$ be Archimedean Riesz spaces and $ℒ_{b} (L, M)$ be the ordered vector space of all order bounded operators from $L$ into $M$ . We define a Lamperti Riesz subspace of $ℒ_{b} (L, M)$ to be an ordered vector subspace $ℒ$ of $ℒ_{b} (L, M)$ such that the elements of $ℒ$ preserve disjointness and any pair of operators in $ℒ$ has a supremum in $ℒ_{b} (L, M)$ that belongs to $ℒ$ . It turns out that the lattice operations in any Lamperti Riesz subspace $ℒ$ of $ℒ_{b} (L, M)$ are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem...

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

Liliana Forzani, Emanuela Sasso, Roberto Scotto (2015)

Studia Mathematica

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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.

Remark on the inequality of F. Riesz

W. Łenski (2005)

Banach Center Publications

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We prove F. Riesz’ inequality assuming the boundedness of the norm of the first arithmetic mean of the functions ${| φ ₙ |}^{p}$ with p ≥ 2 instead of boundedness of the functions φₙ of an orthonormal system.

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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Remark On Fatou-Riesz's Theorem

Vojislav G. Avakumović (1955)

Publications de l'Institut Mathématique

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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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On Riesz homomorphisms in unital $f$ -algebras

Elmiloud Chil (2009)

Mathematica Bohemica

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The main topic of the first section of this paper is the following theorem: let $A$ be an Archimedean $f$ -algebra with unit element $e$ , and $T A \to A$ a Riesz homomorphism such that $T^{2} (f) = T (f T (e))$ for all $f \in A$ . Then every Riesz homomorphism extension $\tilde{T}$ of $T$ from the Dedekind completion $A^{δ}$ of $A$ into itself satisfies ${\tilde{T}}^{2} (f) = \tilde{T} (f T (e))$ for all $f \in A^{δ}$ . In the second section this result is applied in several directions. As a first application it is applied to show a result about extensions of positive projections to the Dedekind completion....

Characterization of Globally Lipschitz Nemytskiĭ Operators Between Spaces of Set-Valued Functions of Bounded φ-Variation in the Sense of Riesz

N. Merentes, J. L. Sánchez Hernández (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let (X,∥·∥) and (Y,∥·∥) be two normed spaces and K be a convex cone in X. Let CC(Y) be the family of all non-empty convex compact subsets of Y. We consider the Nemytskiĭ operators, i.e. the composition operators defined by (Nu)(t) = H(t,u(t)), where H is a given set-valued function. It is shown that if the operator N maps the space $R V_{φ ₁} ([a, b]; K)$ into $R W_{φ ₂} ([a, b]; C C (Y))$ (both are spaces of functions of bounded φ-variation in the sense of Riesz), and if it is globally Lipschitz, then it has to be of the form H(t,u(t))...

A short proof on lifting of projection properties in Riesz spaces

Marek Wójtowicz (1999)

Commentationes Mathematicae Universitatis Carolinae

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Let $L$ be an Archimedean Riesz space with a weak order unit $u$ . A sufficient condition under which Dedekind [ $σ$ -]completeness of the principal ideal $A_{u}$ can be lifted to $L$ is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of $C (X)$ -spaces. Similar results are obtained for the Riesz spaces $B_{n} (T)$ , $n = 1, 2, \dots$ , of all functions of the $n$ th Baire class on a metric space $T$ .

On vectorial inner product spaces

João de Deus Marques (2000)

Czechoslovak Mathematical Journal

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Let $E$ be a real linear space. A vectorial inner product is a mapping from $E \times E$ into a real ordered vector space $Y$ with the properties of a usual inner product. Here we consider $Y$ to be a $ℬ$ -regular Yosida space, that is a Dedekind complete Yosida space such that $⋂_{J \in ℬ} J = {0}$ , where $ℬ$ is the set of all hypermaximal bands in $Y$ . In Theorem 2.1.1 we assert that any $ℬ$ -regular Yosida space is Riesz isomorphic to the space $B (A)$ of all bounded real-valued mappings on a certain set $A$ . Next we prove Bessel Inequality...