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

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 < ∞ .

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 : = ∫ 0 R d E λ f , R ≥ 0 , denote the associated “spherical partial sums,” where ℒ = ∫ 0 ∞ 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 → ∞ under the assumption log ( 2 + ℒ ) f ∈ 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 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 ∂ x α ∂ ξ β a ( x , ξ ) are bounded for, roughly, 4 ≤ | α | + | β | ≤ n + 4 + ϵ . To obtain such results and others, we first prove an abstract result which...