$L^p$-improving properties of measures supported on curves on the Heisenberg group
Volume 132 / 1999
Studia Mathematica 132 (1999), 179-201
DOI: 10.4064/sm-132-2-179-201
Abstract
$L^p$-$L^q$ boundedness properties are obtained for operators defined by convolution with measures supported on certain curves on the Heisenberg group. We find the curvature condition for which the type set of these operators can be the full optimal trapezoid with vertices A=(0,0), B=(1,1), C=(2/3,1/2), D=(1/2,1/3). We also give notions of right curvature and left curvature which are not mutually equivalent.
