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 norm, at Lebesgue points and almost everywhere. We also prove localization results.
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 , aux points de Lebesgue et presque partout. On prouve aussi des résultats de localisation.
@article{AIF_1981__31_4_115_0, author = {Mauceri, Giancarlo}, title = {Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators}, journal = {Annales de l'Institut Fourier}, pages = {115--140}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, number = {4}, year = {1981}, doi = {10.5802/aif.851}, zbl = {0455.35039}, mrnumber = {84h:35125}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.851/} }
TY - JOUR AU - Mauceri, Giancarlo TI - Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators JO - Annales de l'Institut Fourier PY - 1981 SP - 115 EP - 140 VL - 31 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.851/ DO - 10.5802/aif.851 LA - en ID - AIF_1981__31_4_115_0 ER -
%0 Journal Article %A Mauceri, Giancarlo %T Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators %J Annales de l'Institut Fourier %D 1981 %P 115-140 %V 31 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.851/ %R 10.5802/aif.851 %G en %F AIF_1981__31_4_115_0
Mauceri, Giancarlo. Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators. Annales de l'Institut Fourier, Volume 31 (1981) no. 4, pp. 115-140. doi : 10.5802/aif.851. https://aif.centre-mersenne.org/articles/10.5802/aif.851/
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