Arkiv för Matematik

, Volume 51, Issue 2, pp 345–361 | Cite as

Duality and distance formulas in spaces defined by means of oscillation

  • Karl-Mikael PerfektEmail author


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 Q K -spaces, weighted spaces, Lipschitz–Hölder spaces and rectangular \(\operatorname{BMO}\) of several variables.


Banach Space Bergman Space Bloch Space Invariant Space Weighted Bergman Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Institut Mittag-Leffler 2012

Authors and Affiliations

  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden

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