Spectral multipliers on Heisenberg-Reiter and related groups
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| 003 | CHVBK | ||
| 005 | 20210128100536.0 | ||
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0414-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0414-6 | ||
| 100 | 1 | |a Martini |D Alessio |u Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24118, Kiel, Germany |4 aut | |
| 245 | 1 | 0 | |a Spectral multipliers on Heisenberg-Reiter and related groups |h [Elektronische Daten] |c [Alessio Martini] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Nilpotent Lie groups |2 nationallicence | |
| 690 | 7 | |a Heisenberg-Reiter groups |2 nationallicence | |
| 690 | 7 | |a Spectral multipliers |2 nationallicence | |
| 690 | 7 | |a Sublaplacians |2 nationallicence | |
| 690 | 7 | |a Mihlin-Hörmander multipliers |2 nationallicence | |
| 690 | 7 | |a Singular integral operators |2 nationallicence | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1135-1155 |x 0373-3114 |q 194:4<1135 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0414-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0414-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Martini |D Alessio |u Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24118, Kiel, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1135-1155 |x 0373-3114 |q 194:4<1135 |1 2015 |2 194 |o 10231 | ||