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Proceedings of the American Mathematical Society

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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
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.


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