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Bounded mean oscillation and regulated martingales

Name: Bounded mean oscillation and regulated martingales
Creator: Carl S. Herz
Keywords: Probability measures on topological spaces, Maximal functions, Littlewood-Paley theory, 4. Education, 0101 mathematics, 16. Peace & justice, 01 natural sciences, \(H^p\)-classes

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1974Publisher:American Mathematical Society (AMS)Journal:Transactions of the American Mathematical Society, volume 193, pages 199-215 (issn: 0002-9947, eissn: 1088-6850,

Authors: Carl S. Herz;

doi: 10.1090/s0002-9947-1974-0353447-5 , 10.2307/1996909

Bounded mean oscillation and regulated martingales

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Abstract

In the martingale context, the dual Banach space to H 1 {H_1} is BMO in analogy with the result of Charles Fefferman [4] for the classical case. This theorem is an easy consequence of decomposition theorems for H 1 {H_1} -martingales which involve the notion of L p {L_p} -regulated L 1 {L_1} -martingales where 1 > p ≤ ∞ 1 > p \leq \infty . The strongest decomposition theorem is for p = ∞ p = \infty , and this provides full information about BMO. The weaker p = 2 p = 2 decomposition is fundamental in the theory of martingale transforms.

Keywords

Probability measures on topological spaces, Maximal functions, Littlewood-Paley theory, \(H^p\)-classes

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