单位球中Dirichlet空间上的总体紧性

The collective compactness on Dirichlet space in the unit ball

紧算子的性质与有限维空间中的矩阵很类似,在积分方程和许多数学物理问题的研究中起着核心作用.函数空间上的算子序列的总体紧性一直是人们关注的问题.文章考虑了单位球中Dirichlet空间上的To-eplitz算子序列与Hankel算子序列的总体紧性,并给出了总体紧性的充分条件.

The properties of compact operators are analogous to that of matrixes in finite spaces,which play a critical role in the study of integral equations and mathematical physics.And the collectively compact of operator sequence on function spaces has been concerned.In this paper,the author considers collective compactness of Toeplitz operator sequence and Hankel operator sequence on Dirichlet space in the unit ball,and gives the characterization of the operator sequence induced essentially by bounded measurable function.