Analogues of Korn’s inequality on Heisenberg groups

An Isoperimetric Inequality for the Heisenberg Groups

We show that the Heisenberg groups H 2n+1 of dimension ve and higher, considered as Rieman-nian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area L 2). This implies several important results about isoperimetric inequalities for discrete groups that act either on H 2n+1 or on complex hyperbolic space, and provides interesting ex...

On the Heisenberg-weyl Inequality

In 1927, W. Heisenberg demonstrated the impossibility of specifying simultaneously the position and the momentum of an electron within an atom.The well-known second moment Heisenberg-Weyl inequality states: Assume that f : R → C is a complex valued function of a random real variable x such that f ∈ L(R). Then the product of the second moment of the random real x for |f | and the second moment o...

Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

The study of partial differential operators constructed from noncommutative vector fields satisfying the Hörmander condition 1 has hadmuch development. We refer to 2, 3 and the references therein for a systematic account of the study. Recently there have been considerable interests in studying the sub-Laplacians as square sums of vector fields that are not invariant or do not satisfy the Hörman...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

A Stochastic Heisenberg Inequality

An analogue of the Fourier transform will be introduced for all square integrable continuous martingale processes whose quadratic variation is deterministic. Using this transform we will formulate and prove a stochastic Heisenberg inequality.