We study minimal integrability conditions via Luxemburg-type expressions with respect to generalized oscillations that imply the membership of a given function f to the space BMO. Our method is simple, sharp and flexible enough to be adapted to several different settings, like spaces of homogeneous type, non doubling measures on R-n and also BMO spaces defined over more general bases than the basis of cubes. (c) 2021 Elsevier Inc. All rights reserved.
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