An Identity Related to the Riesz Transforms on the Heisenberg Group
نویسندگان
چکیده
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 “missing transform” R2n+1 such that ∑2n+1 j=1 R 2 j = −I in analogy of the classical result ∑n j=1 R 2 j = −I in R.
منابع مشابه
Riesz transforms on groups of Heisenberg type
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