HARDY OPERATORS AND COMMUTATORS ON GENERALIZED CENTRAL FUNCTION SPACES

In this paper, we would like to study the boundedness of operators of Hardy type on generalized central function spaces, such as the generalized central Hardy space HAp phi (Rn), the generalized central Morrey space Mp phi(Rn), and the generalized central Campanato space CMOp phi (Rn), with p E (1,infinity), and phi(t) : (0,infinity)-iota (0,infinity). We first show that HAp'phi (Rn) is the predual of CMOp phi (Rn). After that, we investigate the boundedness of operators of Hardy type on those spaces. By duality, we obtain the boundedness characterization of function b E CMOp phi (Rn) via the Mp phi (Rn)-boundedness of commutator [b, H *].