EUDML

We compute the heat kernel on the classical and nonisotropic Heisenberg groups, and on the free step two nilpotent groups $N_{n, 2}$ , by an elementary method, in particular without using Laguerre calculus.

Means on $C V_{p} (G)$ -subspaces of $C V_{p} (G)$ with RNP and Schur property

Françoise Lust-Piquard — 1989

Annales de l'institut Fourier

Let $G$ be a locally compact abelian group and $C V_{p} (G)$ $(1 \leq p \leq 2)$ be the space of bounded convolution operators: $L^{p} (G) \to L^{p} (G)$ . We generalize to $C V_{p} (G)$ some results which are well known for $C V_{2} (G)$ (or rather for $L^{\infty} (\hat{G})$ ): we define and study “invariant means” on $C V_{p} (G)$ , and we show that if $E \subset G$ is compact and scattered the space $C V_{p} (E)$ (convolution operators which are supported on $E$ ) has the Schur property and is the norm closure of finitely supported measures. We also give some consequences of these results.

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Etude d'ensembles de Ditkin fort dans les algèbres tensorielles et les algèbres de groupe.

Produits tensoriels injectifs d'espaces de Sidon

Produits tensoriels projectifs d'espaces de Banach faiblement séquentiellement complets

L'espace des fonctions presque-périodiques dont le spectre est contenu dans un ensemble compact dénombrable a la propriété de Schur

Produits tensoriels injectifs d'espaces faiblement séquentiellement complets

Lower bounds on //K...//1...... For some contractions K of L² (...), with applications to Markov operators.

Bohr local properties of $C_{Λ} (T)$

Éléments ergodiques et totalement ergodiques dans $L^{\infty} (Γ)$

A simple-minded computation of heat kernels on Heisenberg groups

Means on $C V_{p} (G)$ -subspaces of $C V_{p} (G)$ with RNP and Schur property

Riesz transforms on generalized Heisenberg groups and Riesz transforms associated to the Cheat flow.

Some applications of geometry of Banach spaces to harmonic analysis

Functions in $L^{\infty} (G)$ and associated convolution operators

Opérateurs sur un espace $L^{1}$