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Weighted estimates for the Hankel-, $$\underline{K}$$- and $$Y$$- transformations. (English) Zbl 0808.44008
The author derives sufficient conditions on the pair of nonnegative functions $$u$$ and $$v$$ for the validity of the inequality $\left[ \int^ \infty_ 0 \bigl | u(x) (Tf)(x) \bigr |^ q dx \right]^{1/q} \leq C \left[ \int^ \infty_ 0 \bigl | v(x) f(x) \bigr |^ pdx \right]^{1/p},$ for $$0<q<p$$ and $$p>1$$, where $$T$$ is the Hankel-, the $$\underline {K}$$-, or the $$Y$$-transformation.
##### MSC:
 44A15 Special integral transforms (Legendre, Hilbert, etc.) 26D10 Inequalities involving derivatives and differential and integral operators
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