caa a22 4500 605496366 CHVBK 20210128100536.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10231-014-0414-6 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0414-6 Martini Alessio Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24118, Kiel, Germany aut Spectral multipliers on Heisenberg-Reiter and related groups [Elektronische Daten] [Alessio Martini] Let $$L$$ L be a homogeneous sublaplacian on a $$2$$ 2 -step stratified Lie group $$G$$ G of topological dimension $$d$$ d and homogeneous dimension $$Q$$ Q . By a theorem due to Christ and to Mauceri and Meda, an operator of the form $$F(L)$$ F ( L ) is bounded on $$L^p$$ L p for $$1 < p < \infty $$ 1 < p < ∞ if $$F$$ F satisfies a scale-invariant smoothness condition of order $$s > Q/2$$ s > Q / 2 . Under suitable assumptions on $$G$$ G and $$L$$ L , here we show that a smoothness condition of order $$s > d/2$$ s > d / 2 is sufficient. This extends to a larger class of $$2$$ 2 -step groups the results for the Heisenberg and related groups by Müller and Stein and by Hebisch and for the free group $$N_{3,2}$$ N 3 , 2 by Müller and the author. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Nilpotent Lie groups nationallicence Heisenberg-Reiter groups nationallicence Spectral multipliers nationallicence Sublaplacians nationallicence Mihlin-Hörmander multipliers nationallicence Singular integral operators nationallicence Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1135-1155 0373-3114 194:4<1135 2015 194 10231 https://doi.org/10.1007/s10231-014-0414-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0414-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Martini Alessio Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24118, Kiel, Germany aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1135-1155 0373-3114 194:4<1135 2015 194 10231