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Another Characterization of BMO

Another characterization of BMO

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jun 1980Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 79, page 249 (issn: 0002-9939,

Authors: R. R. Coifman; Richard Rochberg;

doi: 10.2307/2043245 , 10.1090/s0002-9939-1980-0565349-8

Another Characterization of BMO

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Abstract

The following characterization of functions of bounded mean oscillation (BMO) is proved. f is in BMO if and only if \[ f = α log ⁡ g ∗ − β log ⁡ h ∗ + b f = \alpha \log {g^ \ast } - \beta \log {h^ \ast } + b \] where g ∗ , ( h ∗ ) {g^ \ast },({h^ \ast }) is the Hardy-Littlewood maximal function of g, (h), respectively, b is bounded and ‖ f ‖ BMO ⩽ c ( α + β + ‖ b ‖ ∞ ) {\left \| f \right \|_{{\text {BMO}}}} \leqslant c(\alpha + \beta + {\left \| b \right \|_\infty }) .

Keywords

Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, Hardy-Littlewood maximal function, functions of bounded mean oscillation

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