The Nehari-Schwarz lemma and infinitesimal boundary rigidity of bounded holomorphic functions

DOI10.24193/SUBBMATH.2022.2.05arXiv2206.04346OpenAlexW4283035046MaRDI QIDQ6401556

Publication date: 9 June 2022

Abstract: We survey a number of recent generalizations and sharpenings of Nehari's extension of Schwarz' lemma for holomorphic self-maps of the unit disk. In particular, we discuss the case of infinitely many critical points and its relation to the zero sets and invariant subspaces for Bergman spaces, as well as the case of equality at the boundary.

Full work available at URL: https://doi.org/10.24193/subbmath.2022.2.05

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Bergman spaces of functions in several complex variables (32A36)

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