Almost Everywhere Convergence  Of Convolution Powers Without Finite Second Moment

Christopher M. Wedrychowicz

Displaying similar documents to “Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment”

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 $log (2 + ℒ) f \in L^{2} (G) .$

Embedding theorems for Müntz spaces

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2011)

Annales de l’institut Fourier

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We discuss boundedness and compactness properties of the embedding $M_{Λ}^{1} \subset L^{1} (μ)$ , where $M_{Λ}^{1}$ is the closed linear span of the monomials $x^{λ_{n}}$ in $L^{1} ([0, 1])$ and $μ$ is a finite positive Borel measure on the interval $[0, 1]$ . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $Λ$ . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators...

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...

Fourier Transforms of Measures and Algebraic Relations on Their Supports

Thomas W. Körner (2009)

Annales de l’institut Fourier

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We investigate the relation between the rate of decrease of a Fourier transform and the possible algebraic relations on its support.

Commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1994)

Commentationes Mathematicae Universitatis Carolinae

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The commutative neutrix convolution product of the functions $x^{r} e_{-}^{λ x}$ and $x^{s} e_{+}^{μ x}$ is evaluated for $r, s = 0, 1, 2, ...$ and all $λ, μ$ . Further commutative neutrix convolution products are then deduced.