Hardy spaces with variable exponents on RD-spaces and applications

In this article, the authors introduce Hardy spaces with variable exponents, H*(,p(.)) (chi), on RD-spaces with infinite measures via the grand maximal function. Then the authors characterize these spaces by means of the non-tangential maximal function or the dyadic maximal function. Characterizations in terms of atoms or Littlewood-Paley functions are also established. As applications, the authors prove an Olsen inequality for fractional integral operators and the boundedness of singular integral operators and quasi-Banach valued sublinear operators on these spaces. Finally, a duality theory of these spaces is developed.