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

We investigate the Lp(0,∞)−Lq(0,∞)Lp(0,∞)−Lq(0,∞) mapping properties of the operatorsLν,μαf(y)=yμ∫0∞(xy)νf(x)Jα(xy)dx,f∈C0∞(0,+∞), for suitable values of the parameters, and we evaluate the operator norm of Lν,μα in some special and significant cases.