Geodesic
Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations
Archivum mathematicum, Tome 30 (1994) no. 1, pp. 29-43 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We give conditions on pairs of non-negative functions $u$ and $v$ which are sufficient that, for $01$ \[ \left[ \int _0^\infty |u(x)(Tf)(x)|^q\, dx\right]^{\frac{1}{q}} \le C\left[ \int _0^\infty |v(x)f(x)|^p\, dx\right]^{\frac{1}{p}}\,, \] where $T$ is the Hankel-, K-, or the Y-transformations.
We give conditions on pairs of non-negative functions $u$ and $v$ which are sufficient that, for $0$, $p>1$ \[ \left[ \int _0^\infty |u(x)(Tf)(x)|^q\, dx\right]^{\frac{1}{q}} \le C\left[ \int _0^\infty |v(x)f(x)|^p\, dx\right]^{\frac{1}{p}}\,, \] where $T$ is the Hankel-, K-, or the Y-transformations.
Classification : 26D10, 26D15, 42B10, 44A15
Keywords: weighted inequalities; Hankel; K- and Y-transformations 
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     author = {Emara, Salah A. A.},
     title = {Weighted estimates for the {Hankel-,} $\underline{K}$- and $Y$- transformations},
     journal = {Archivum mathematicum},
     pages = {29--43},
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     volume = {30},
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     zbl = {0808.44008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1994_30_1_a4/}
}
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Emara, Salah A. A. Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations. Archivum mathematicum, Tome 30 (1994) no. 1, pp. 29-43. http://geodesic.mathdoc.fr/item/ARM_1994_30_1_a4/

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