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The spaces $ H\sp p(B\sb n), \;0<p<1,$ and $ B\sb {pq}(B\sb n),\;0<p<q<1,$ are not locally convex


Author: Ji Huai Shi
Journal: Proc. Amer. Math. Soc. 103 (1988), 69-74
MSC: Primary 46E10; Secondary 32A35
DOI: https://doi.org/10.1090/S0002-9939-1988-0938646-9
MathSciNet review: 938646
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Abstract: In this note, we use the Ryll-Wojtaszczyk polynomials to prove that the spaces $ {H^p}\left( {{B_n}} \right),0 < p < 1$, and $ {B_{pq}}\left( {{B_n}} \right),0 < p < q < 1$, fail to be locally convex.


References [Enhancements On Off] (What's this?)

  • [1] S. Bochner, Classes of holomorphic functions of several variables in circular domains, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 721-723. MR 0120390 (22:11144)
  • [2] A. E. Livingston, The space $ {H^p},0 < p < 1$, is not normable, Pacific J. Math. 3 (1953), 613-616. MR 0056191 (15:38d)
  • [3] J. Mitchell and K. T. Hahn, Representation of linear functionals in $ {H^p}$ spaces over bounded symmetric domains in $ {C^n}$, J. Math. Anal. Appl. 56 (1976), 379-396. MR 0427696 (55:727)
  • [4] W. Rudin, Functional analysis, McGraw-Hill, 1973. MR 0365062 (51:1315)
  • [5] J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), 107-116. MR 684495 (84f:32004)

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DOI: https://doi.org/10.1090/S0002-9939-1988-0938646-9
Article copyright: © Copyright 1988 American Mathematical Society

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