ON CRITICAL CASES OF SOBOLEV’S INEQUALITIES FOR HEISENBERG GROUPS

We prove some Trudinger-type inequalities and Brezis-Gallouet-Wainger inequality on the Heisenberg group, extending to this context the Euclidean results by T. Ozawa.     

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU（2,2）/S（U（2） × U（2））

Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.     

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Let G=SU(2.2).K=S(U(2)×U(2)),and for l∈Z.let{τ_l}_(leZ) be a one- dimensional K-type and let E_l be the line bundle over G/K associated toτ_l .It is shown thal theτ_l-spher cal function on G is given by the hypergeometric functions of several variables.By applying this result,a central limit theorem for the space G/K is obtained.     

H型群上的非线性Liouville定理

对H型群上的次线性方程ΔGu up=0进行了研究,其中ΔG是对应的sublaplace算子．通过将移动平面方法推广到H型群上,证明了在一定条件下的p和函数u,次线性方程ΔGu up=0的唯一解是u≡0．     

H型群上的非线性Liouville定理

对H型群上的次线性方程△Gu+up=0进行了研究,其中△G是对应的sublaplace算子.通过将移动平面方法推广到H型群上,证明了在一定条件下的p和函数u,次线性方程△Gu+up=0的唯一解是u≡0.     

四元Heisenberg群上的一个半线性问题

本文研究了四元Heisenberg群上的一个半线性方程问题,通过把对应的方程问题化为积分进行估计,证明了其对应的半线性方程的非负双椭圆解只有唯一的零解,推广了相应Heisenberg群上的定理.