# Note on semigroups generated by positive Rockland operators on graded homogeneous groups

Jacek Dziubański; Waldemar Hebisch; Jacek Zienkiewicz

Studia Mathematica (1994)

- Volume: 110, Issue: 2, page 115-126
- ISSN: 0039-3223

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topDziubański, Jacek, Hebisch, Waldemar, and Zienkiewicz, Jacek. "Note on semigroups generated by positive Rockland operators on graded homogeneous groups." Studia Mathematica 110.2 (1994): 115-126. <http://eudml.org/doc/216104>.

@article{Dziubański1994,

abstract = {Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let $p_t$ be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that $|p_1(x)| ≤ Cexp(-cτ(x)^\{d/(d-1)\})$. Moreover, if G is not stratified, more precise estimates of $p_1$ at infinity are given.},

author = {Dziubański, Jacek, Hebisch, Waldemar, Zienkiewicz, Jacek},

journal = {Studia Mathematica},

keywords = {fundamental solution; upper bounds; kernel estimates; Rockland operator; homogeneous Lie group; convolution kernel; left-invariant differential operator},

language = {eng},

number = {2},

pages = {115-126},

title = {Note on semigroups generated by positive Rockland operators on graded homogeneous groups},

url = {http://eudml.org/doc/216104},

volume = {110},

year = {1994},

}

TY - JOUR

AU - Dziubański, Jacek

AU - Hebisch, Waldemar

AU - Zienkiewicz, Jacek

TI - Note on semigroups generated by positive Rockland operators on graded homogeneous groups

JO - Studia Mathematica

PY - 1994

VL - 110

IS - 2

SP - 115

EP - 126

AB - Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let $p_t$ be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that $|p_1(x)| ≤ Cexp(-cτ(x)^{d/(d-1)})$. Moreover, if G is not stratified, more precise estimates of $p_1$ at infinity are given.

LA - eng

KW - fundamental solution; upper bounds; kernel estimates; Rockland operator; homogeneous Lie group; convolution kernel; left-invariant differential operator

UR - http://eudml.org/doc/216104

ER -

## References

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