On positive Rockland operators
Colloquium Mathematicum, Tome 67 (1994) no. 2, pp. 197-216
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on $L_p(G;dg)$. Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on $L_2$ we prove that it is closed on each of the $L_p$-spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the $L_p$-spaces, p ∈ [1,∞]. Further extensions of these results to nonhomogeneous operators and general representations are also given.
Affiliations des auteurs :
Pascal Auscher 1 ; A. ter Elst 1 ; Derek Robinson 1
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author = {Pascal Auscher and A. ter Elst and Derek Robinson},
title = {On positive {Rockland} operators},
journal = {Colloquium Mathematicum},
pages = {197--216},
publisher = {mathdoc},
volume = {67},
number = {2},
year = {1994},
doi = {10.4064/cm-67-2-197-216},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-67-2-197-216/}
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TY - JOUR AU - Pascal Auscher AU - A. ter Elst AU - Derek Robinson TI - On positive Rockland operators JO - Colloquium Mathematicum PY - 1994 SP - 197 EP - 216 VL - 67 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-67-2-197-216/ DO - 10.4064/cm-67-2-197-216 LA - en ID - 10_4064_cm_67_2_197_216 ER -
Pascal Auscher; A. ter Elst; Derek Robinson. On positive Rockland operators. Colloquium Mathematicum, Tome 67 (1994) no. 2, pp. 197-216. doi: 10.4064/cm-67-2-197-216
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