| Title:
|
Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations (English) |
| Author:
|
Emara, Salah A. A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
29-43 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
weighted inequalities |
| Keyword:
|
Hankel |
| Keyword:
|
K- and Y-transformations |
| MSC:
|
26D10 |
| MSC:
|
26D15 |
| MSC:
|
42B10 |
| MSC:
|
44A15 |
| idZBL:
|
Zbl 0808.44008 |
| idMR:
|
MR1282111 |
| . |
| Date available:
|
2008-06-06T21:25:33Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107493 |
| . |
| Reference:
|
[1] Benedetto, J. J., Heinig, H. P., Johnson, R.: Weighted Hardy spaces and the Laplace transform II.Math. Nachr. 132 (1987), 29-55. MR 0910042 |
| Reference:
|
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| Reference:
|
[3] Emara, S.: A class of weighted inequalities.Harmonic Analysis, ICM-90 Satelite conf. Proc., Japan 1990, Springer-Verlag (1991). Zbl 0772.46011, MR 1261432 |
| Reference:
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[4] Erdelyi, A.(Ed.): Tables of integral transforms.vol. II, McGraw Hill, New York, 1954. Zbl 0058.34103, MR 0065685 |
| Reference:
|
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| Reference:
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| Reference:
|
[7] Hardy, G. H., Littlewood, J. E., Polya, G.: Inequalities.Cambridge Univ. Press, 1967. |
| Reference:
|
[8] Heinig, H.P.: Interpolation of quasi-normed spaces involving weights.Canad. Math. Soc. Conf. Proc. 1 (1981), 245-267. Zbl 0561.46036, MR 0670108 |
| Reference:
|
[9] Heinig, H. P.: Weighted norm inequalities for classes of operators.Indiana Univ. Math. J. 33 (1984), 573-582. Zbl 0511.46031, MR 0749315 |
| Reference:
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[10] Heywood, P., Rooney, P. G.: A weighted norm inequality for the Hankel transformation.Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 45-50. MR 0781084 |
| Reference:
|
[11] Johnson, R.: Temperatures, Riesz potentials and Lipschitz spaces of Herz.Proc. London Math. Soc. (3) 27 (1973), 290-316. MR 0374895 |
| Reference:
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[12] Kalugina, T. F.: 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 |
| Reference:
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| Reference:
|
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| . |
