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Local to global results for spaces of \({{\mathrm{BMO}}}\) type

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Abstract

We study a class of spaces, \(JN_p\), related to \({{\mathrm{BMO}}}\) in the abstract setting of a metric space with a doubling measure. We obtain a Reimann–Rychener type local to global result and also show that a Boman type condition is sufficient to make the embedding of \(JN_p\) into weak \(L^{p}\) to hold. We discuss certain necessary condition. Our abstract setting covers various situations at once and, in particular, includes all geodesic spaces.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Niko Marola

  2. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076, Aalto, Finland

    Olli Saari

Authors
  1. Niko Marola
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  2. Olli Saari
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Correspondence to Olli Saari.

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The authors were supported by the Academy of Finland.

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Marola, N., Saari, O. Local to global results for spaces of \({{\mathrm{BMO}}}\) type. Math. Z. 282, 473–484 (2016). https://doi.org/10.1007/s00209-015-1549-x

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  • DOI: https://doi.org/10.1007/s00209-015-1549-x

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