具有加权测度的H型群上漂移Laplace算子的Levitin-Parnovski型特征值不等式
LEVITIN-PARNOVSKI-TYPE INEQUALITY FOR EIGENVALUES OF THE DRIFTING LAPLACIAN ON THE H-TYPE GROUP WITH THE WEIGHTED MEASURE

本文研究了具有加权测度dμ=e-φdv的H型群G上漂移Laplace算子-△G+<▽Gφ，▽G（·）>的Dirichlet特征值问题，建立了该问题的Levitin-Parnovski型特征值不等式，推广包含了Ilias和Makhoul对Heisenberg群上次Laplace算子所获得的结果（J.Geom.Anal.，2012，22（1）：206-222）.
In this paper, we study the Dirichlet eigenvalue problem of the drifting Laplacian -△G + <▽Gφ, ▽G (·)> on the H-type group G with the weighted measured dμ=e-φdv. We establish a Levitin-Parnovski universal inequality for eigenvalues of this problem, which generalize the result derived by Ilias and Makhoul for the Kohn Laplacian on the Heisenberg group (J. Geom. Anal., 2012, 22(1):206-222)