کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
840591 | 908485 | 2012 | 13 صفحه PDF | دانلود رایگان |
Let Hn=R2n×RHn=R2n×R be the nn-dimensional Heisenberg group, ∇Hn∇Hn be its sub-elliptic gradient operator, and ρ(ξ)=(|z|4+t2)1/4ρ(ξ)=(|z|4+t2)1/4 for ξ=(z,t)∈Hnξ=(z,t)∈Hn be the distance function in HnHn. Denote Q=2n+2Q=2n+2 and Q′=Q/(Q−1)Q′=Q/(Q−1). It is proved in this paper that there exists a positive constant α∗α∗ such that for any pair ββ and αα satisfying 0≤β
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 12, August 2012, Pages 4483–4495