# Heat kernels and Riesz transforms on nilpotent Lie groups

A. ter Elst; Derek Robinson; Adam Sikora

Colloquium Mathematicae (1998)

- Volume: 74, Issue: 2, page 191-218
- ISSN: 0010-1354

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topter Elst, A., Robinson, Derek, and Sikora, Adam. "Heat kernels and Riesz transforms on nilpotent Lie groups." Colloquium Mathematicae 74.2 (1998): 191-218. <http://eudml.org/doc/210510>.

@article{terElst1998,

abstract = {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.},

author = {ter Elst, A., Robinson, Derek, Sikora, Adam},

journal = {Colloquium Mathematicae},

keywords = {subellipticity; comparison operator; Gaussian bounds; Riesz operators; Lipschitz spaces; Harnack-type inequalities},

language = {eng},

number = {2},

pages = {191-218},

title = {Heat kernels and Riesz transforms on nilpotent Lie groups},

url = {http://eudml.org/doc/210510},

volume = {74},

year = {1998},

}

TY - JOUR

AU - ter Elst, A.

AU - Robinson, Derek

AU - Sikora, Adam

TI - Heat kernels and Riesz transforms on nilpotent Lie groups

JO - Colloquium Mathematicae

PY - 1998

VL - 74

IS - 2

SP - 191

EP - 218

AB - 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.

LA - eng

KW - subellipticity; comparison operator; Gaussian bounds; Riesz operators; Lipschitz spaces; Harnack-type inequalities

UR - http://eudml.org/doc/210510

ER -

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