Guliyev, EminEroglu, AhmetMammadov, Yagub2019-08-012019-08-0120101085-3375https://dx.doi.org/10.1155/2010/976493https://hdl.handle.net/11480/4930We consider the generalized shift operator, associated with the Dunkl operator Lambda(alpha)(f)(x) = (d/dx)f(x) + ((2 alpha + 1)/x)((f(x) - f(-x))/2), alpha > -1/2. We study the boundedness of the Dunkltype fractional maximal operator M(beta) in the Dunkl-type Morrey space L(p,lambda,alpha)(R), 0 <= lambda < 2 alpha + 2. We obtain necessary and sufficient conditions on the parameters for the boundedness M(beta), 0 <= beta < 2 alpha + 2 from the spaces L(p,lambda,alpha)(R) to the spaces L(q,lambda,alpha)(R), 1 < p <= q < infinity, and from the spaces L(1,lambda,alpha)(R) to the weak spaces WL(q,lambda,alpha)(R), 1 < q < infinity. As an application of this result, we get the boundedness of M beta from the Dunkl-type Besov-Morrey spaces Bp theta,lambda,alpha s(R) to the spaces Bq theta,lambda,alpha s(R), 1 < p <= q < infinity, 0 <= lambda < 2 alpha + 2, 1/p - 1/q = beta/(2 alpha + 2 - lambda), 1 <= theta <= infinity, and 0 < s < 1.eninfo:eu-repo/semantics/openAccessArticle10.1155/2010/9764932-s2.0-77955387211Q4WOS:000280762600001Q1