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On the shape of the unit sphere in $ Q(\Delta)$


Author: Lisa R. Goldberg
Journal: Proc. Amer. Math. Soc. 118 (1993), 1179-1185
MSC: Primary 46E15; Secondary 30Fxx, 46E22
DOI: https://doi.org/10.1090/S0002-9939-1993-1186987-7
MathSciNet review: 1186987
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Abstract: We show that the unit sphere in the Banach space of $ {L^1}$ holomorphic quadratic differentials on the disk is weakly uniformly convex with exponent $ 1/2$ at certain points.


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  • [A] S. Axler, Bergman spaces and their operators, Surveys of Some Recent Results in Operator Theory (J. Conway and B. Morrel, eds.), Pitman Res. Notes Math. Ser., vol. 171, Longman Sci. Tech., Harlow, 1988. MR 958569 (90b:47048)
  • [D] J. Diestel, Geometry of Banach spaces--selected topics, Springer Verlag, New York, 1975. MR 0461094 (57:1079)
  • [Ga] F. P. Gardiner, Teichmüller theory and quadratic differentials, Wiley, New York, 1987. MR 903027 (88m:32044)
  • [FR] R. Forelli and W. Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593-602. MR 0357866 (50:10332)
  • [Mc] C. T. McMullen, Amenability, Poincaré series and quasiconformal maps, Invent. Math. 97 (1989), 95-127. MR 999314 (90e:30048)
  • [R] H. L. Royden, Automorphisms and isometries of Teichmüller space, Ann. of Math. Stud., vol. 66, Princeton Univ. Press, Princeton, NJ, 1971, pp. 368-384. MR 0288254 (44:5452)
  • [S] K. Strebel, Quadratic differentials, Springer-Verlag, New York, 1984. MR 743423 (86a:30072)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1186987-7
Article copyright: © Copyright 1993 American Mathematical Society

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