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XV: 18, 259-277, LNM 850 (1981)

**BRU, Bernard**; **HEINICH, Henri**; **LOOTGIETER, Jean-Claude**

Autour de la dualitÃ© $(H^1,BMO)$ (Martingale theory)

This is a sequel to 1330. Given two martingales $(X,Y)$ in $H^1$ and $BMO$, it is investigated whether their duality functional can be safely estimated as $E[X_{\infty}Y_{\infty}]$. The simple result is that if $X_{\infty}Y_{\infty}$ belongs to $L^1$, or merely is bounded upwards by an element of $L^1$, then the answer is positive. The second (and longer) part of the paper searches for subspaces of $H^1$ and $BMO$ such that the property would hold between their elements, and here the results are fragmentary (a question of 1330 is answered). An appendix discusses a result of Talagrand

Keywords: $BMO$, $H^1$ space, Hardy spaces

Nature: Original

Retrieve article from Numdam

XLVII: 02, xxxi-l, LNM 2137 (2015)

**BRU, Bernard**

Marc et le dossier Doeblin

Nature: History

Autour de la dualitÃ© $(H^1,BMO)$ (Martingale theory)

This is a sequel to 1330. Given two martingales $(X,Y)$ in $H^1$ and $BMO$, it is investigated whether their duality functional can be safely estimated as $E[X_{\infty}Y_{\infty}]$. The simple result is that if $X_{\infty}Y_{\infty}$ belongs to $L^1$, or merely is bounded upwards by an element of $L^1$, then the answer is positive. The second (and longer) part of the paper searches for subspaces of $H^1$ and $BMO$ such that the property would hold between their elements, and here the results are fragmentary (a question of 1330 is answered). An appendix discusses a result of Talagrand

Keywords: $BMO$, $H^1$ space, Hardy spaces

Nature: Original

Retrieve article from Numdam

XLVII: 02, xxxi-l, LNM 2137 (2015)

Marc et le dossier Doeblin

Nature: History