New Results on the Equivalence of K -Functionals and Modulus of Continuity of Functions Defined on the Sobolev Space Constructed by the Generalized Jacobi-Dunkl Operator

Abstract

In this paper, we establish some new generalized results on the equivalence of $K$ -functionals and modulus of continuity of functions defined on the Sobolev space $L_{\alpha ,\beta }^2\left(ℝ\right)$ , by using the harmonic analysis related to the Jacobi-Dunkl operator ${\Delta }_{\alpha ,\beta }$ , where $\alpha \ge \beta \ge -1/2$ and $\alpha \ne -1/2$ .