# On positive Rockland operators

Pascal Auscher; A. ter Elst; Derek Robinson

Colloquium Mathematicae (1994)

- Volume: 67, Issue: 2, page 197-216
- ISSN: 0010-1354

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topAuscher, Pascal, ter Elst, A., and Robinson, Derek. "On positive Rockland operators." Colloquium Mathematicae 67.2 (1994): 197-216. <http://eudml.org/doc/210273>.

@article{Auscher1994,

abstract = {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.},

author = {Auscher, Pascal, ter Elst, A., Robinson, Derek},

journal = {Colloquium Mathematicae},

keywords = {fundamental solution; homogeneous Lie group; homogeneous operator; positive Rockland operator; homogeneous differential operator},

language = {eng},

number = {2},

pages = {197-216},

title = {On positive Rockland operators},

url = {http://eudml.org/doc/210273},

volume = {67},

year = {1994},

}

TY - JOUR

AU - Auscher, Pascal

AU - ter Elst, A.

AU - Robinson, Derek

TI - On positive Rockland operators

JO - Colloquium Mathematicae

PY - 1994

VL - 67

IS - 2

SP - 197

EP - 216

AB - 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.

LA - eng

KW - fundamental solution; homogeneous Lie group; homogeneous operator; positive Rockland operator; homogeneous differential operator

UR - http://eudml.org/doc/210273

ER -

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