Abstract
$BMO$, the space of functions of bounded mean oscillation, was first introduced by F. John and L. Nirenberg in 1961. It became a focus of attention when C. Fefferman proved that $BMO$ is the dual of the (real) Hardy space $H^1$ in 1971. In the past 30 years, this space was studied extensively by many mathematicians. With the help of $BMO$, many phenomena can be characterized clearly. In this review we discuss the connections between $BMO$ functions, the sharp function operator, Carleson measures, atomic decompositions and commutator operators in $\mathbf{R}^n$. We strive to cover some of the main developments in the theory, including $BMO$ in a bounded Lipschitz domain in $\mathbf{R}^n$ and in the product space $\mathbf{R} \times \mathbf{R}$.
Citation
Der-Chen Chang. Cora Sadosky. "FUNCTIONS OF BOUNDED MEAN OSCILLATION." Taiwanese J. Math. 10 (3) 573 - 601, 2006. https://doi.org/10.11650/twjm/1500403848
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