An analogue of Hardy's theorem for the Heisenberg group
Volume 87 / 2001
Colloquium Mathematicum 87 (2001), 137-145
MSC: Primary 43A30; Secondary 43A10, 22E25.
DOI: 10.4064/cm87-1-9
Abstract
We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on $ {\mathbb R}^n $ related to them.
