(L_p, L_q) Boundedness of the fractional maximal operator associated with the Dunkl operator on the real line

摘要

On the real line, the Dunkl operators are differential-difference operators associated with the reflection group ?_2 on ?. In this paper, we obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional maximal operator associated with the Dunkl operator on ? from the spaces L_(p,α)(?) to the spaces L_(q,α)(?) and from the spaces L_(1,α)(?) to the weak spaces WL_(q,α)(?).