On the duality of some martingale spaces

Fefferman has proved that the dual space of the martingale Hardy space H1 is the BMO1-space. Garsia went further and proved that the dual of Hp is the so-called martingale Kp-space, where p and q are two conjugate numbers and 1 ≤ p < 2. The martingale Hardy spaces HΦ with general Young function Φ...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1992-02, Vol.45 (1), p.43-52
Main Authors: Bassily, N.L., Abdel-Fattah, A.M.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic processes
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Summary:Fefferman has proved that the dual space of the martingale Hardy space H1 is the BMO1-space. Garsia went further and proved that the dual of Hp is the so-called martingale Kp-space, where p and q are two conjugate numbers and 1 ≤ p < 2. The martingale Hardy spaces HΦ with general Young function Φ, were investigated by Bassily and Mogyoródi. In this paper we show that the dual of the martingale Hardy space HΦ is the martingale Hardy space HΦ where (Φ, Ψ) is a pair of conjugate Young functions such that both Φ and Ψ have finite power. Moreover, two other remarkable dualities are presented.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700036996