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