Distortion of sets by inner functions

Author:
D. H. Hamilton

Journal:
Proc. Amer. Math. Soc. **117** (1993), 771-774

MSC:
Primary 30A10; Secondary 30D50

DOI:
https://doi.org/10.1090/S0002-9939-1993-1139469-2

MathSciNet review:
1139469

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Abstract: For any inner function with and any Borel set

**[1]**C. Belna, W. Cohn, G. Piranian, and K. Stephenson,*Level sets of special infinite products*, Michigan Math. J.**29**(1982), 79-81. MR**646373 (83h:30033)****[2]**J. Fernandez and D. Pestana,*Distortion of boundary sets under inner functions and applications*(to appear). MR**1183352 (93k:30014)****[3]**D. H. Hamilton,*Conformal distortion of boundary sets*, Trans. Amer. Math. Soc.**308**(1988), 69-81. MR**946430 (90h:30020)****[4]**P. W. Jones,*Bounded holomorphic functions with all level sets of infinite length*, Michigan Math. J.**27**(1980), 197-208. MR**555839 (81b:30066)****[5]**G. Piranian and A. Weitsman,*Level sets of infinite length*, Comment. Math. Helv.**53**(1978), 166-164. MR**490872 (81j:30029)****[6]**M. Tsuji,*Potential theory in modern function theory*, Maruzen, Tokyo, 1959. MR**0114894 (22:5712)**

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1139469-2

Article copyright:
© Copyright 1993
American Mathematical Society