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October 19, 2025Open Access

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

Key Points

Dunkl-type fractional integral operators are shown to be bounded from L^p to L^q spaces under certain conditions.
The extended results apply to generalized Dunkl-type Morrey spaces and Dunkl-type BMOϕ spaces.
The paper investigates the boundedness of these operators primarily in Dunkl-type Campanato spaces.
Findings indicate important implications for the study of fractional operators in functional spaces.

Abstract

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 1p - 1q = βd_α. In spsa, the authors introduced the generalized Dunkl-type fractional integral operator T_ρ^α and it's modified version T_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.

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