Copyright © 2010 Emin Guliyev et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the generalized shift operator, associated with the Dunkl operator , . We study the boundedness of the Dunkl-type fractional maximal operator in the Dunkl-type Morrey space , . We obtain necessary and sufficient conditions on the parameters for the boundedness , from the spaces to the spaces , , and from the spaces to the weak spaces , . As an application of this result, we get the boundedness of from the Dunkl-type Besov-Morrey spaces to the spaces , , , , , and .