en fr Harmonic analysis on graphs and Lie groups : quadratic functionals, Riesz transforms and Besov spaces Analyse harmonique sur les graphes et les groupes de Lie : fonctionnelles quadratiques, transformées de Riesz et espacesReport as inadecuate




en fr Harmonic analysis on graphs and Lie groups : quadratic functionals, Riesz transforms and Besov spaces Analyse harmonique sur les graphes et les groupes de Lie : fonctionnelles quadratiques, transformées de Riesz et espaces - Download this document for free, or read online. Document in PDF available to download.

1 IF - Institut Fourier

Abstract : This thesis is devoted to results in real harmonic analysis in discrete graphs or continuous Lie groups geometric contexts.Let $\Gamma$ be a graph a set of vertices and edges equipped with a discrete laplacian $\Delta=I-P$, where $P$ is a Markov operator.Under suitable geometric assumptions on $\Gamma$, we show the $L^p$ boundedness of fractional Littlewood-Paley functionals. We introduce $H^1$ Hardy spaces of functions and of $1$-differential forms on $\Gamma$, giving several characterizations of these spaces, only assuming the doubling property for the volumes of balls in $\Gamma$. As a consequence, we derive the $H^1$ boundedness of the Riesz transform. Assuming furthermore pointwise upper bounds for the kernel Gaussian of subgaussian upper bounds on the iterates of the kernel of $P$, we also establish the $L^p$ boundedness of the Riesz transform for $1



Author: Joseph Feneuil -

Source: https://hal.archives-ouvertes.fr/



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