We give conditions on pairs of non-negative weight functions
uand vwhich are sufficient that, for 1<p, q <∞,
Tis the Hankel-or the K-transformation.
The proofs are based on a weighted Marcinkiewicz interpolation theorem for linear operators. In the case that
Tis the Hankel transformation and 1<p≦q <∞, the result is similar to a weighted estimate of Heywood and Rooney , but with different weight conditions.