Abstract
The paper is devoted to the study of Fefferman–Stein inequalities for stochastic integrals. If is a martingale, is the stochastic integral, with respect to , of some predictable process taking values in , then for any weight belonging to the class we have the estimates and The proofs rest on the Bellman function method: the inequalities are deduced from the existence of certain special functions, enjoying appropriate majorization and concavity. As an application, related statements for Haar multipliers are indicated. The above estimates can be regarded as probabilistic counterparts of the recent results of Lerner, Ombrosi and Perez concerning singular integral operators.
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