No abstract

No abstract

Using a generalized translation operator, we obtain a generalization of Titchmarsh's theorem of the Jacobi transform for functions satisfying the ψ-Jacobi Lipschitz condition.

Using a generalized Dunkl translation, we obtain an analog of Theorem 5.2 in Younis' paper [2] for the Dunkl transform for functions satisfying the (δ, γ)-Dunkl Lipschitz condition in the space L 2 (R, |x| 2α+1 dx).

We consider a singular differential operator on the real line .we establish Miyachi's theorems for the generalized Fourier transform on R tied the Differential-difference operator .