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| The Presentation Problem of the Conjugate Cone of the Hardy Space Hp (0 < p ≤ 1) |
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Citation： |
Jianyong WANG.The Presentation Problem of the Conjugate Cone of the Hardy Space Hp (0 < p ≤ 1)[J].Chinese Annals of Mathematics B,2013,34(4):541~556 |
| Page view： 1737
Net amount： 1146 |
Authors： |
Jianyong WANG; |
Foundation： |
National Natural Science Foundation of China (No. 10871141). |
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| Abstract： |
The Hardy space Hp is not locally convex if 0 < p < 1, even though its conjugate
space (Hp)? separates the points of Hp. But then it is locally p-convex, and its conjugate
cone (Hp)
?
p is large enough to separate the points of Hp. In this case, the conjugate cone
can be used to replace its conjugate space to set up the duality theory in the p-convex
analysis. This paper deals with the representation problem of the conjugate cone (Hp)?
p of
Hp for 0 < p ≤ 1, and obtains the subrepresentation theorem (Hp)
?
p
L
∞
(T,C
?
p). |
Keywords： |
Locally p-convex space, Hardy space, Normed conjugate cone, Shadow
cone, Subrepresentation theorem |
Classification： |
46A16, 46A20, 32A35, 42B30 |
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