Riesz Potential on the Heisenberg Group

An Identity Related to the Riesz Transforms on the Heisenberg Group

Let {X1, . . . ,X2n,T} be a real basis for the Heisenberg Lie algebra hn. In this paper, we calculate the explicit kernels of the Riesz transforms Rj = XjL 1 2 , j = 1, 2, · · · , 2n on the Heisenberg group Hn. Here L = − ∑2n j=1 X 2 j is the sub-Laplacian operator. We show that ∫∞ −∞Rjdt = Rj for j = 1, 2, · · · , 2n where Rj ’s are the regular Riesz transforms on R . We also construct the “mi...

The Heat Kernel and the Riesz Transforms on the Quaternionic Heisenberg Groups

As the heat kernel plays an important role in many problems in harmonic analysis, an explicit usable expression is very much desirable. An explicit expression for the heat kernel for the Heisenberg group Hn = C ×R was obtained by Hulanicki [9] and by Gaveau [7]. Gaveau [7] also obtained the heat kernel for free nilpotent Lie groups of step two. Cygan [4] obtained the heat kernel for all nilpote...

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...

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

B-FOCAL CURVES OF BIHARMONIC B-GENERAL HELICES IN Heis

In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis   Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis