TY - JOUR
AU - Ruszkowski, Bartosch
PY - 2018/08/06
Y2 - 2024/08/04
TI - Hardy inequalities for the Heisenberg Laplacian on convex bounded polytopes
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 123
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-105218
UR - https://www.mscand.dk/article/view/105218
SP - 101-120
AB - <p>We prove a Hardy-type inequality for the gradient of the Heisenberg Laplacian on open bounded convex polytopes on the first Heisenberg group. The integral weight of the Hardy inequality is given by the distance function to the boundary measured with respect to the Carnot-Carathéodory metric. The constant depends on the number of hyperplanes, given by the boundary of the convex polytope, which are not orthogonal to the hyperplane $x_3=0$.</p>
ER -