ESTIMATES FOR WEIGHTED HARDY-LITTLEWOOD AVERAGES AND THEIR COMMUTATORS ON MIXED CENTRAL MORREY SPACES

In this paper, we study the boundedness of the weighted Hardy-Littlewood average Hq, and its commutator H-phi(b), on mixed central Morrey spaces. More precisely, we first obtain the sufficient and necessary condition for the boundedness of H-phi, on the mixed central Morrey space <(M) over dot>(p)((q) over right arrow) (R-n), and also obtain the sharp constant simultaneously. Then we give a characterization for the boundedness of the commutator formed by H-phi, and a central bounded mean oscillation function b on <(M) over dot>(p)((q) over right arrow)(R-n).