Some characterizations of local bmo and $h^{1}$ on spaces of homogeneous type (Harmonic Analysis and Nonlinear Partial Differential Equations)

Abstract

In this paper we generalize some results on the local bmo and Hardy space h^{1}, shown in [18] for doubling metric-measure spaces, to the setting of spaces of homogeneous type. These include a John-Nirenberg inequality for bmo, proved using a good-lambda inequality as well as by duality, the boundedness of the Hardy-Littlewood maximal function on bmo, and a characterization of h^{1} in terms of an atomic decomposition with an approximate moment condition on the atoms, together with the corresponding mean oscillation condition for bmo.