In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.
A transference theorem for convolution operators is proved for certain families of one-dimensional hypergroups.
We show that the transference method of Coifman and Weiss can be extended to Hardy and Sobolev spaces. As an application we obtain the de Leeuw restriction theorems for multipliers.
By using the notion of contraction of Lie groups, we transfer estimates for joint spectral projectors from the unit complex sphere in to the reduced Heisenberg group hⁿ. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on hⁿ. As a consequence, we prove, in the spirit of Sogge’s work, a discrete restriction theorem for the sub-Laplacian L on hⁿ.
By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.
Dans cet article on étudie en premier lieu la résolvante (le noyau de Green) d’un opérateur agissant sur un arbre localement fini. Ce noyau est supposé invariant par un groupe d’automorphismes de l’arbre. On donne l’expression générique de cette résolvante et on établit des simplifications sous différentes hypothèses sur .En second lieu on introduit la transformation de Poisson qui associe à une mesure additive finie sur l’espace des bouts de l’arbre une fonction propre de l’ opérateur. On...