We prove that, for a distinguished laplacian on an Iwasawa AN group corresponding to a complex semisimple Lie group, a Hörmander type multiplier theorem holds. Our argument is based on Littlewood-Paley theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-14, author = {W. Hebisch}, title = {H\"ormander type multiplier theorem on complex Iwasawa AN groups}, journal = {Colloquium Mathematicae}, volume = {120}, year = {2010}, pages = {587-591}, zbl = {1195.22006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-14} }
W. Hebisch. Hörmander type multiplier theorem on complex Iwasawa AN groups. Colloquium Mathematicae, Tome 120 (2010) pp. 587-591. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-14/