A Beurling type theorem in weighted Bergman spaces

作者：Ball Joseph A^*; Bolotnikov Vladimir

来源：Comptes Rendus Mathematique, 2013, 351(11-12): 433-436.

DOI：10.1016/j.crma.2013.06.004

For the vector-valued Hardy space H-2(u) and the standard weighted Bergman space A(n)(y) with coefficient Hilbert spaces u and y, we single out a class of contractive multipliers from H-2(u) to A(n)(y) which we call partially isometric multipliers. We then show that a closed subspace M subset of A(n)(y) is invariant under the shift operator S-n : f (z) bar right arrow zf(z) if and only if M = Phi. H-2(u) for some partially isometric multiplier Phi from H-2(u) to A(n) (u).

• 出版日期2013-6
• 单位美国弗吉尼亚理工大学(Virginia Tech)