## Arkiv för Matematik

• Ark. Mat.
• Volume 51, Number 2 (2013), 345-361.

### Duality and distance formulas in spaces defined by means of oscillation

Karl-Mikael Perfekt

#### Abstract

For the classical space of functions with bounded mean oscillation, it is well known that $\operatorname{VMO}^{**} = \operatorname{BMO}$ and there are many characterizations of the distance from a function f in $\operatorname{BMO}$ to $\operatorname{VMO}$. When considering the Bloch space, results in the same vein are available with respect to the little Bloch space. In this paper such duality results and distance formulas are obtained by pure functional analysis. Applications include general Möbius invariant spaces such as QK-spaces, weighted spaces, Lipschitz–Hölder spaces and rectangular $\operatorname{BMO}$ of several variables.

#### Article information

Source
Ark. Mat., Volume 51, Number 2 (2013), 345-361.

Dates
Revised: 20 April 2012
First available in Project Euclid: 1 February 2017

https://projecteuclid.org/euclid.afm/1485907220

Digital Object Identifier
doi:10.1007/s11512-012-0175-7

Mathematical Reviews number (MathSciNet)
MR3090201

Zentralblatt MATH identifier
1283.46011

Rights

#### Citation

Perfekt, Karl-Mikael. Duality and distance formulas in spaces defined by means of oscillation. Ark. Mat. 51 (2013), no. 2, 345--361. doi:10.1007/s11512-012-0175-7. https://projecteuclid.org/euclid.afm/1485907220

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