Abstract
We study, in the setting of a doubling metric measure space, the local bmo space and Hardy space h1 defined by Goldberg. We state a John–Nirenberg type inequality for the local bmo space and give two proofs, via a good-lambda inequality and via duality. We also prove the boundedness of the Hardy–Littlewood maximal function from bmo to bmo. Finally, we give characterizations of bmo and h1 using alternative mean-oscillation and moment conditions.
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