Arkiv för Matematik

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

Duality and distance formulas in spaces defined by means of oscillation

Karl-Mikael Perfekt

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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.

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

Received: 23 June 2011
Revised: 20 April 2012
First available in Project Euclid: 1 February 2017

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2012 © Institut Mittag-Leffler


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.

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