On the Lp − Lq norm of the Hankel transform and related operators

We investigate the Lp(0,∞)− Lq(0,∞) mapping properties of the operators Lαν ,μ f (y) = yμ ∞ 0 (xy)ν f (x) Jα(xy)dx, f ∈ C∞0 (0,+∞), for suitable values of the parameters, and we evaluate the operator norm of Lαν ,μ in some special and significant cases.