Heisenberg群H^n上的有界变差函数  

BV FUNCTIONS IN THE HEISENBERG GROUP H^n

作　　者：宋迎清[1] 杨孝平[2] 

机构地区：[1]湖南城市学院数学与计算科学系,湖南益阳413000 [2]南京理工大学理学院,南京210094

出　　处：《数学年刊（A辑）》2003年第5期541-554,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19771048)

摘　　要：本文有四个目标:一是研究了H-Caccioppoli集的几何性质;二是证明了H^n上有界变差函数u的跳跃集J_u是H-Rectifiable并刻画不连续集S_u和跳跃集J_u的特征;三是证明了u在Ω上几乎处处近似可微并研究u的逐点行为;最后还证明了D_Hu作为Radon测度能分解成三部分,即D_Hu=L_u·^(2n+1)+2w_(2n-1)/w_(2n+1)(u^+-u^-)v_uS_d^(Q-1)J_u+_H^cu,其中L_u ∈ R^(2n)是u的近似微分,u^+,u^-,v_u分别是u在跳跃点的近似上、下极限和跳跃方向。There are four goals: the first is to investigate some geometric properties of H-Cacciop-poli sets, the second is to prove that for u ∈ BVH(Ω) its jump set Ju is H-Rectifiable and to characterize discontinuity set Su and jump set Ju, the third is to prove that u ∈ BVH(Ω) is approximately differentiate a.e. in Ω and investigate pointwise behavior of u, while the last and the most important is to show that DHU as a Radon measure can be split into three parts. Namely, is the approximate differential of u, and u+, u-, vu are respectively the approximate upper limit, approximate lower limit and jump direction of u at a jump point.

关 键 词：有界变差函数 HEISENBERG群 Radon测度分解 H—Rectifiability 近似微分 

分 类 号：O152[理学—数学]