Vector-valued sub-Bergman spaces on the unit disk

Release time:2025-04-11

Journal:202502 Submitted to Mathematische Zeitschrift

Abstract:We initiate the study of vector-valued sub-Bergman spaces on the unit disk, which are de Branges-Rovnyak subspaces of the vector-valued weighted Bergman space A2α,E, deffned by the contractions TB or T∗B for an analytic multiplier B of A2 α,E. There are notable differences between the scalar and vector-valued cases, especially when E is inffnite-dimensional.Throughout this work, we ffll in some gaps and provide uniffed proofs for several results from the scalar case. Most of our proofs are more elementary and straightforward.

Co-author:Caixing Gu, Shuaibing Luo, Pan Ma

Indexed by:Journal paper

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

Translation or Not:no