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$\mathit{BMO}$ spaces for nondoubling metric measure spaces

Dariusz Kosz

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In this article we study the family of $\mathit{BMO}^p$ spaces, $p \geq 1$, in the general context of metric measure spaces. We give a characterization theorem that allows to describe all possible relations between these spaces considered as sets of functions. Examples illustrating the obtained cases and some additional results related to the John-Nirenberg inequality are also included.


The author is supported by the National Science Centre of Poland, project no. 2016/ 21/N/ST1/01496.

Article information

Publ. Mat., Volume 64, Number 1 (2020), 103-119.

Received: 2 February 2018
Revised: 5 July 2018
First available in Project Euclid: 3 January 2020

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 42B35: Function spaces arising in harmonic analysis 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

$\mathit{BMO}$ space metric measure space non-doubling measure John-Nirenberg inequality


Kosz, Dariusz. $\mathit{BMO}$ spaces for nondoubling metric measure spaces. Publ. Mat. 64 (2020), no. 1, 103--119. doi:10.5565/PUBLMAT6412004.

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