Boundedness from $H^1$ to $L^1$ of Riesz transforms on a Lie group of exponential growth

Peter Sjögren; Maria Vallarino

Displaying similar documents to “Boundedness from $H^{1}$ to $L^{1}$ of Riesz transforms on a Lie group of exponential growth”

Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

Steve Hofmann, Marius Mitrea, Sylvie Monniaux (2011)

Annales de l’institut Fourier

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We prove $L^{p}$ -bounds for the Riesz transforms associated to the Hodge-Laplacian equipped with absolute and relative boundary conditions in a Lipschitz subdomain of a (smooth) Riemannian manifold for $p$ in a certain interval depending on the Lipschitz character of the domain.

Riesz transforms for Dunkl transform

Bechir Amri, Mohamed Sifi (2012)

Annales mathématiques Blaise Pascal

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In this paper we obtain the $L^{p}$ -boundedness of Riesz transforms for the Dunkl transform for all $1 < p < \infty$ .

A.e. convergence of spectral sums on Lie groups

Christopher Meaney, Detlef Müller, Elena Prestini (2007)

Annales de l’institut Fourier

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Let $ℒ$ be a right-invariant sub-Laplacian on a connected Lie group $G,$ and let $S_{R} f : = \int_{0}^{R} d E_{λ} f, R \geq 0,$ denote the associated “spherical partial sums,” where $ℒ = \int_{0}^{\infty} λ d E_{λ}$ is the spectral resolution of $ℒ .$ We prove that $S_{R} f (x)$ converges a.e. to $f (x)$ as $R \to \infty$ under the assumption $log (2 + ℒ) f \in L^{2} (G) .$

On the Fefferman-Phong inequality

Abdesslam Boulkhemair (2008)

Annales de l’institut Fourier

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We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by $\frac{n}{2} + 4 + ϵ$ improving thus the bound $2 n + 4 + ϵ$ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type $S_{0, 0}^{0}$ , we show that this number is bounded by $n + 4 + ϵ$ ; more precisely, for a non negative symbol $a$ , the Fefferman-Phong inequality holds if $\partial_{x}^{α} \partial_{ξ}^{β} a (x, ξ)$ are bounded for, roughly, $4 \leq | α | + | β | \leq n + 4 + ϵ$ . To obtain such results and others, we first prove an abstract result which...

Displaying similar documents to “Boundedness from H 1 to L 1 of Riesz transforms on a Lie group of exponential growth”

Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

Riesz transforms for Dunkl transform

A.e. convergence of spectral sums on Lie groups

On the Fefferman-Phong inequality

Displaying similar documents to “Boundedness from $H^{1}$ to $L^{1}$ of Riesz transforms on a Lie group of exponential growth”