XII: 16, 138-147, LNM 649 (1978)
LÉPINGLE, Dominique
Sur certains commutateurs de la théorie des martingales (Martingale theory)
Let $\beta$ the operator on (closed) martingales $X$ consisting in multiplication of $X_{\infty}$ by a given r.v. $B$. One investigates the commutator $J\beta-\beta J$ of $\beta$ with some operator $J$ on martingales (a typical example is stochastic integration $JX=H.X$ where $H$ is a given bounded previsible process), expecting this commutator to be bounded in $L^p$ if $B$ belongs to $BMO$. This is indeed true under natural conditions on $J$
Keywords: $BMO$
Nature: Original
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