超Poincaré不等式在L^p空间上的推广及应用

Generalization and Application of Super-Poincare Inequality on L^p-space

该文建立了Lp(μ)空间上的超Poincare不等式,得到了Lp(μ)上半群的半紧性和紧性的充要条件及相应的扰动结果,同时给出超Poincare不等式成立的一个充分条件,推广了L2(μ)上的相关结论.作为应用,文中最后讨论了黎曼流形上一类非对称扩散算子的本质谱.

The authors establish the super-Poincare inequality on L^p-space with respect to a measure space, and obtain some necessary and sufficient conditions about semicompact and compact property of semigroup and the perturbation result. Meanwhile, a sufficient condition for super-Poincare inequality is shown, which generalizes some known results obtained on the L^2-space. As applications, the essential spectrum of a class of non-symmetric diffusion operators on Riemannian manifold is studied.