Fix λ > 0. Consider the Bessel operator λ := − d 2 dx 2 − 2λ x d dx on R + , where R + := (0, ∞) and dm λ := x 2λ dx with dx the Lebesgue measure. We provide a deeper study of the Bessel Riesz transform and fractional integral operator via the related Besov and Triebel–Lizorkin spaces associated with λ. Moreover, we investigate some possible characterization of the commutator of fractional integral operator, which was missing in the literature of the Bessel setting.
MSC Classification 2010: 42B30, 42B20, 42B35