On the Boundedness of Generalized Fractional Integral Operators in Morrey Spaces and Camapanato Spaces associated with the Dunkl Operator on the Real line

It is known that the Dunkl-type fractional integral operator I_β (0 < β< 2α+ 2 =d_α) is bounded from Lᵖ(,dμ_α) to Lq (, dμ_α) when 1 < p < d_αβ and 1/p - 1/q = βd_α. In {spsa} , the authors introduced the generalized Dunkl-type fractional integral operator T_ρ^α and it's modified version T̃_ρ^α and extended the above boundedness results to the generalized Dunkl-type Morrey spaces and Dunkl-type BMO_ϕ spaces. In this paper we investigate the boundedness of generalized Dunkl-type fractional integral operators and it's modified version mainly on the Dunkl-type Campanato space.