Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators

Mauceri, Giancarlo

Annales de l'Institut Fourier, Tome 31 (1981) no. 4, pp. 115-140.

On étudie les sommes de Riesz pour les développements en fonctions propres pour une classe d’opérateurs hypoelliptiques sur le groupe de Heisenberg. Les opérateurs que l’on considère sont homogènes et invariants par l’action du gorupe unitaire. On obtient des résultats de convergence en norme $L^p$, aux points de Lebesgue et presque partout. On prouve aussi des résultats de localisation.

We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in $L^p$ norm, at Lebesgue points and almost everywhere. We also prove localization results.

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