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BMO from dyadic BMO on the bidisc
Journal of the London Mathematical Society, 2008AbstractWe generalize to the bidisc a theorem of Garnett and Jones relating the space BMO of functions of bounded mean oscillation to its martingale counterpart, dyadic BMO. Namely, translation‐averages of suitable families of dyadic BMO functions belong to BMO.
Jill Pipher, Lesley A. Ward
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Properties of BMO Functions whose Reciprocals are also BMO
Zeitschrift für Analysis und ihre Anwendungen, 1993The paper gives some properties of the space \(\text{BMO}_ *=\{w\in\text{BMO}: 1/\omega\in\text{BMO}\}\) such as Theorem 1. A real- valued function \(u\) is in \(\text{BMO }\Leftrightarrow\) there exists \(w\in \text{BMO}_ *\) such that \(u=w-1/w\) (a consequence of \(\text{Lip }\alpha\)-operatability on BMO); Theorem 3.
Johnson, R. L., Neugebauer, C. J.
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