AN INTERPOLATION THEOREM FOR SUBLINEAR OPERATORS ON NON-HOMOGENEOUS METRIC MEASURE SPACES

Let (chi, d, mu) be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors establish an interpolation result that a sublinear operator which is bounded from the Hardy space H-1(mu) to L-1,L-infinity(mu) and from L-infinity(mu) to the BMO-type space RBMO(mu) is also bounded on L-P(mu) for all p is an element of (1, infinity). This extension is not completely straightforward and improves the existing result.