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On the duality of some martingale spaces

Published online by Cambridge University Press:  17 April 2009

N.L. Bassily  and
A.M. Abdel-Fattah
N.L. Bassily
Affiliation:
Department of Mathematics, American University of Cairo, P.O. Box 2511 Cairo, Egypt
A.M. Abdel-Fattah
Affiliation:
The Institute of Statistical Studies, Cairo University, Cairo, Egypt
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 1 , February 1992 , pp. 43 - 52
Copyright
Copyright © Australian Mathematical Society 1992

References

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