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    STUDIA MATHEMATICA - Issue no. 2 / 2022  
         
  Article:   THE NEHARI--SCHWARZ LEMMA AND INFINITESIMAL BOUNDARY RIGIDITY OF BOUNDED HOLOMORPHIC FUNCTIONS.

Authors:  OLIVER ROTH.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath. 2022.2.05

Published Online: 2022-06-10
Published Print: 2022-06-30
pp. 285-294

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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.

Key words: Schwarz'' lemma, Blaschke products, Bergman spaces

Mathematics Subject Classification (2010): 30C80, 32A36
 
         
     
         
         
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