Copyright © 2010 Emin V. Guliyev and Yagub Y. Mammadov. 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 some embeddings into the Morrey space (-Morrey space) , and modified Morrey space (modified -Morrey space) associated with the Dunkl operator on . As applications we get boundedness of the fractional maximal operator , , associated with the Dunkl operator (fractional -maximal operator) from the spaces to for and from the spaces to for .