Local hardy and BMO spaces on non-homogeneous spaces

Let mu be a Radon measure on R-d which may be non doubling. The only condition that A must satisfy is the size condition mu(B(x, r)) <= Cr-n for some fixed n epsilon (0, d]. Recently, Tolsa introduced the spaces RBMO(mu) and H-atb(1,infinity)(mu), which, in some ways, play the role of the classical spaces BMO and H-1 in case A is a doubling measure. In this paper, the author considdrs the local versions of the spaces RBMO(mu) and H-atb(1,infinity)(mu) in the sense of Goldberg and establishes the connections between the spaces RBMO(mu) and H-atb(1,infinity)(mu) with their local versions. An interpolation result of linear operators is also given.