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Another characterization of BMO. (English) Zbl 0432.42016

Summary: The following characterization of functions of bounded mean oscillation (BMO) is proved. \(f\) is in BMO if and only if \[ f = \alpha \log g^* - \beta \log h^* +b \] where \(g^*\), \((h^*)\) is the Hardy-Littlewood maximal function of \(g\), \((h)\), respectively, \(b\) is bounded and \(\| f \| _{\text{BMO}} \leq c(\alpha + \beta + \| b\|_\infty)\).

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
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