二维单位球上不同加权Dirichlet空间之间的总体紧复合算子列

Collectively compact composition operators sequences on weighted Dirichlet spaces in the unit ball of C^2

设φ_n:B→B是一全纯映射列并且是单叶的,φ_n(0)=0,φ_n的Frechet导数是有界的,并且|J_(φ_z(z))|≠0且有界,C_(φ_n):D_α~2(B,dv_α)→D_β~2(B,dv_B)(α,β>2/(2+1))是一致有界线性复合算子列。作者利用测度给出了此复合算子列的总体紧性。

Suppose φ_n:B→B is a sequence of holomorphic and univalent functions, φ_n(0)=0, and the Frechet derivative of φ_n is bounded, |J_(φ_n)(z)|≠0,C_(φ_n):D_α~2(B,dv_α)→D_β~2(B,dv_β)(α,β>2/(2+1)) is a sequence of uniform bounded composition operators, the collective compactness of the operators sequences with the measure is investigated.