Weighted estimates for the Hankel-, - and - transformations
Archivum Mathematicum (1994)
- Volume: 030, Issue: 1, page 29-43
- ISSN: 0044-8753
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topEmara, Salah A. A.. "Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations." Archivum Mathematicum 030.1 (1994): 29-43. <http://eudml.org/doc/247557>.
@article{Emara1994,
abstract = {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.},
author = {Emara, Salah A. A.},
journal = {Archivum Mathematicum},
keywords = {weighted inequalities; Hankel; K- and Y-transformations; -transform; -transform; Hankel transform; nonnegative functions; inequality},
language = {eng},
number = {1},
pages = {29-43},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Weighted estimates for the Hankel-, $\underline\{K\}$- and $Y$- transformations},
url = {http://eudml.org/doc/247557},
volume = {030},
year = {1994},
}
TY - JOUR
AU - Emara, Salah A. A.
TI - Weighted estimates for the Hankel-, $\underline{K}$- and $Y$- transformations
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 1
SP - 29
EP - 43
AB - 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.
LA - eng
KW - weighted inequalities; Hankel; K- and Y-transformations; -transform; -transform; Hankel transform; nonnegative functions; inequality
UR - http://eudml.org/doc/247557
ER -
References
top- Weighted Hardy spaces and the Laplace transform II, Math. Nachr. 132 (1987), 29-55. (1987) MR0910042
- Weighted norm inequalities for the Hankel- and K̲-transformations, Proc. Roy. Soc. Edinburgh Sect A 103 (1986), 325-333. (1986) MR0866845
- A class of weighted inequalities, Harmonic Analysis, ICM-90 Satelite conf. Proc., Japan 1990, Springer-Verlag (1991). Zbl0772.46011MR1261432
- Tables of integral transforms, vol. II, McGraw Hill, New York, 1954. (1954) Zbl0058.34103MR0065685
- 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) Zbl0389.46024MR0512275
- Inequalities, Cambridge Univ. Press, 1967. (1967)
- Interpolation of quasi-normed spaces involving weights, Canad. Math. Soc. Conf. Proc. 1 (1981), 245-267. (1981) Zbl0561.46036MR0670108
- Weighted norm inequalities for classes of operators, Indiana Univ. Math. J. 33 (1984), 573-582. (1984) Zbl0511.46031MR0749315
- A weighted norm inequality for the Hankel transformation, Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 45-50. (1984) MR0781084
- Temperatures, Riesz potentials and Lipschitz spaces of Herz, Proc. London Math. Soc. (3) 27 (1973), 290-316. (1973) MR0374895
- 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). MR0407616
- Sobolev spaces, Springer-Verlag, Berlin, 1985. (1985) Zbl0692.46023MR0817985
- A weighted gradient inequality, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), 329-335. (1989) Zbl0686.26004MR1007530
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