Abstract
The Hardy space H p is not locally convex if 0 < p < 1, even though its conjugate space (H p)* separates the points of H p. But then it is locally p-convex, and its conjugate cone (H p) p * is large enough to separate the points of H p. 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 (H p) * p of H p for 0 < p ≤ 1, and obtains the subrepresentation theorem (H p) * p ≃ L ∞(T, C * p ).
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Project supported by the National Natural Science Foundation of China (No. 10871141).
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Wang, J. The presentation problem of the conjugate cone of the Hardy space H p (0 < p ≤ 1). Chin. Ann. Math. Ser. B 34, 541–556 (2013). https://doi.org/10.1007/s11401-013-0781-0
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DOI: https://doi.org/10.1007/s11401-013-0781-0