Boundedness of sublinear operators in Hardy spaces on RD-spaces via atoms ✩

Let p 1 be near to 1 and X be an RD-space, which includes any Carnot–Carathéodory space with a doubling measure. In this paper, the authors prove that a sublinear operator T extends to a bounded sublinear operator from Hardy spaces Hp(X) to some quasi-Banach space B if and only if T maps all (p, 2)-atoms into uniformly bounded elements of B. © 2007 Elsevier Inc. All rights reserved.