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

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...

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...

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

Riesz transforms on groups of Heisenberg type

The aim of this article is to prove the following theorem. Theorem: Let p be in (1,∞), Hn,m a group of Heisenberg type, R the vector of the Riesz transforms on Hn,m. There exists a constant Cp independent of n and m such that for every f ∈ L (Hn,m) C p e ‖f‖Lp(Hn,m) ≤ ‖|Rf |‖Lp(Hn,m) ≤ Cpe‖f‖Lp(Hn,m). It has been proved by F. Lust-Piquard that the operator norm of R does not depend on n (see [L...

Category of $H$-groups

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.