Estimates for Spectral Projection Operators of the Sub-Laplacian on the Heisenberg Group
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چکیده
In this paper, we use Laguerre calculus to find the Lp spectrum (λ, μ) of the pair (L, iT). Here L = −12 ∑n j=1(ZjZj+ZjZj) andT = ∂ ∂t with {Z1, . . . ,Zn,Z1, , . . . ,Zn,T} a basis for the left-invariant vector fields on the Heisenberg group. We find kernels for the spectral projection operators on the ray λ > 0 in the Heisenberg brush and show that they are Calderón-Zygmund-Mikhlin operators. Estimates for these operators in Lpk(Hn), H (Hn), and S p,ν k (Hn) spaces therefore can be deduced.
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تاریخ انتشار 2001