Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations
Emara, Salah A. A.
Archivum Mathematicum, Tome 030 (1994), p. 29-43 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1994-01-01
Classification:  26D10,  26D15,  42B10,  44A15
@article{107493,
     author = {Salah A. A. Emara},
     title = {Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations},
     journal = {Archivum Mathematicum},
     volume = {030},
     year = {1994},
     pages = {29-43},
     zbl = {0808.44008},
     mrnumber = {1282111},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107493}
}
Emara, Salah A. A. Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations. Archivum Mathematicum, Tome 030 (1994) pp. 29-43. http://gdmltest.u-ga.fr/item/107493/

Weighted Hardy spaces and the Laplace transform II, Math. Nachr. 132 (1987), 29-55. (1987) | MR 0910042

Weighted norm inequalities for the Hankel- and K̲-transformations, Proc. Roy. Soc. Edinburgh Sect A 103 (1986), 325-333. (1986) | MR 0866845

A class of weighted inequalities, Harmonic Analysis, ICM-90 Satelite conf. Proc., Japan 1990, Springer-Verlag (1991). | MR 1261432 | Zbl 0772.46011

Tables of integral transforms, vol. II, McGraw Hill, New York, 1954. (1954) | MR 0065685 | Zbl 0058.34103

Tables of integrals, series and products, New York, Academic Press, 1980. (1980)

A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305. (1978) | MR 0512275 | Zbl 0389.46024

Inequalities, Cambridge Univ. Press, 1967. (1967)

Interpolation of quasi-normed spaces involving weights, Canad. Math. Soc. Conf. Proc. 1 (1981), 245-267. (1981) | MR 0670108 | Zbl 0561.46036

Weighted norm inequalities for classes of operators, Indiana Univ. Math. J. 33 (1984), 573-582. (1984) | MR 0749315 | Zbl 0511.46031

A weighted norm inequality for the Hankel transformation, Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 45-50. (1984) | MR 0781084

Temperatures, Riesz potentials and Lipschitz spaces of Herz, Proc. London Math. Soc. (3) 27 (1973), 290-316. (1973) | MR 0374895

Interpolation of Banach spaces with functional parameter, The Reiteration theorem. Vestnik Moskovskoyo University, Ser. 1, Math. Mech. 30(6) (1975) (Engl. Transl. Moscow Univ. Math. Bull. 30 (6) (1975), 108-116). | MR 0407616

Sobolev spaces, Springer-Verlag, Berlin, 1985. (1985) | MR 0817985 | Zbl 0692.46023

A weighted gradient inequality, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), 329-335. (1989) | MR 1007530 | Zbl 0686.26004