Taiwanese Journal of Mathematics

FUNCTIONS OF BOUNDED MEAN OSCILLATION

Der-Chen Chang and Cora Sadosky

Full-text: Open access

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 $\mathbf{R} \times \mathbf{R}$.

Article information

Source
Taiwanese J. Math., Volume 10, Number 3 (2006), 573-601.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403848

Digital Object Identifier
doi:10.11650/twjm/1500403848

Mathematical Reviews number (MathSciNet)
MR2206315

Zentralblatt MATH identifier
1100.42013

Subjects
Primary: 42B30: $H^p$-spaces
Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]

Keywords
bounded mean oscillation Hardy spaces sharp function operator Carleson measures product spaces

Citation

Chang, Der-Chen; Sadosky, Cora. FUNCTIONS OF BOUNDED MEAN OSCILLATION. Taiwanese J. Math. 10 (2006), no. 3, 573--601. doi:10.11650/twjm/1500403848. https://projecteuclid.org/euclid.twjm/1500403848


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