Geodesic
Heat kernels and Riesz transforms on nilpotent Lie groups
Colloquium Mathematicum, Tome 74 (1997) no. 2, pp. 191-218.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian lower bounds and deduce Harnack inequalities valid for all times.
DOI : 10.4064/cm-74-2-191-218

A. ter Elst 1 ; Derek Robinson 1 ; Adam Sikora 1

1 
@article{10_4064_cm_74_2_191_218,
     author = {A. ter Elst and Derek Robinson and Adam Sikora},
     title = {Heat kernels and {Riesz} transforms on nilpotent {Lie} groups},
     journal = {Colloquium Mathematicum},
     pages = {191--218},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {1997},
     doi = {10.4064/cm-74-2-191-218},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-74-2-191-218/}
}
TY  - JOUR
AU  - A. ter Elst
AU  - Derek Robinson
AU  - Adam Sikora
TI  - Heat kernels and Riesz transforms on nilpotent Lie groups
JO  - Colloquium Mathematicum
PY  - 1997
SP  - 191
EP  - 218
VL  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-74-2-191-218/
DO  - 10.4064/cm-74-2-191-218
LA  - en
ID  - 10_4064_cm_74_2_191_218
ER  - 
%0 Journal Article
%A A. ter Elst
%A Derek Robinson
%A Adam Sikora
%T Heat kernels and Riesz transforms on nilpotent Lie groups
%J Colloquium Mathematicum
%D 1997
%P 191-218
%V 74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-74-2-191-218/
%R 10.4064/cm-74-2-191-218
%G en
%F 10_4064_cm_74_2_191_218
A. ter Elst; Derek Robinson; Adam Sikora. Heat kernels and Riesz transforms on nilpotent Lie groups. Colloquium Mathematicum, Tome 74 (1997) no. 2, pp. 191-218. doi : 10.4064/cm-74-2-191-218. http://geodesic.mathdoc.fr/articles/10.4064/cm-74-2-191-218/

Cité par Sources :