Abstract
Starting from a generalized Sonine-type integral representation for the normalized Bessel functions (which was given earlier by Srivastava [H. M. Srivastava, A note on a generalization of Sonine's first finite integral, Matematiche (Catania) 23 (1968), pp. 1-6]), we construct a generalized Sonine (respectively, Sonine-Dunkl) integral transform on R, which turns out (together with its dual) to be intertwining operators between Bessel (respectively, Dunkl) operators and certain singular differential (respectively, differential-difference) operators on R.