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The Grunsky Norm and Some Coefficient Estimates for Bounded Functions
Author(s) -
Grinshpan A. Z.,
Pommerenke CH.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397003524
Subject(s) - mathematics , bounded function , norm (philosophy) , unit disk , operator (biology) , operator norm , bounded operator , mathematics subject classification , pure mathematics , mathematical analysis , law , biochemistry , chemistry , repressor , political science , transcription factor , gene
We estimate the growth order in n of the Taylor coefficients of bounded univalent functions in the unit disk. Our estimate depends on the norm of the Grunsky operator. In particular, we improve the known results for coefficients of quasiconformally extendible univalent functions. 1991 Mathematics Subject Classification 30C50, 30C75, 30C55.