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We give conditions on pairs of non-negative functions $u$ and $v$ which are sufficient that, for $0<q<p$, $p>1$ $${\left[{\int }_0^{\infty }{\left|u\left(x\right)\left(Tf\right)\left(x\right)\right|}^{q}dx\right]}^{\frac{1}{q}}\le C{\left[{\int }_0^{\infty }{\left|v\left(x\right)f\left(x\right)\right|}^{p}dx\right]}^{\frac{1}{p}},$$ where $T$ is the Hankel-, K-, or the Y-transformations.