Artículo
Ombrosi, S.; De Rosa, L. "Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces" (2003) Publicacions Matematiques. 47(1):71-102
Consulte la política de Acceso Abierto del editor
Abstract:
In this paper we introduce the one-sided weighted spaces Lw -(β), -1 < β < 1. The purpose of this definition is to obtain an extension of the Weyl fractional integral operator I α + from Lw p. into a suitable weighted space. Under certain condition on the weight w, we have that L w -(β) coincides with the dual of the Hardy space H- 1 (w). We prove for 0 < β < 1, that L w -(β) consists of all functions satisfying a weighted Lipschitz condition. In order to give another characterization of Lw - (β), 0 ≤ β < 1, we also prove a one-sided version of John-Nirenberg Inequality. Finally, we obtain necessary and sufficient conditions on the weight w for the boundedness of an extension of Iα + from Lw p into L w - (β), -1 < β < 1, and its extension to a bounded operator from Lw - (0) into Lw -(α).
Registro:
| Documento: | Artículo |
| Título: | Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces |
| Autor: | Ombrosi, S.; De Rosa, L. |
| Filiación: | Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Ciudad de Buenos Aires, Argentina |
| Palabras clave: | Weighted BMO; Weighted Lebesgue and Lipschitz spaces; Weigths; Weyl fractional integral |
| Año: | 2003 |
| Volumen: | 47 |
| Número: | 1 |
| Página de inicio: | 71 |
| Página de fin: | 102 |
| DOI: | http://dx.doi.org/10.5565/PUBLMAT_47103_04 |
| Título revista: | Publicacions Matematiques |
| Título revista abreviado: | Publ. Mat. |
| ISSN: | 02141493 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v47_n1_p71_Ombrosi |
Referencias:
- Harboure, E., Salinas, O., Viviani, B., Boundedness of the fractional integral on weighted Lebesgue and Lipschitz spaces (1997) Trans. Amer. Math. Soc., 349 (1), pp. 235-255
- Macías, R.A., Riveros, M.S., One-sided extrapolation at infinity and singular integrals (2000) Proc. Roy. Soc. Edinburgh Sect. A, 130 (5), pp. 1081-1102
- Martín-Reyes, F.J., New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions (1993) Proc. Amer. Math. Soc., 117 (3), pp. 691-698
- Martín-Reyes, F.J., Pick, L., De La Torre, A., A∞ +condition (1993) Canad. J. Math., 45 (6), pp. 1231-1244
- Martín-Reyes, F.J., De La Torre, A., One-sided BMO spaces (1994) London Math. Soc. (2), 49 (3), pp. 529-542
- Muckenhoupt, B., Wheeden, R.L., Weighted bounded mean oscillation and the Hilbert transform (1975) Studia Math., 54 (3), pp. 221-237
- Muckenhoupt, B., Wheeden, R.L., Weighted norm inequalities for fractional integrals (1974) Trans. Amer. Math. Soc., 192, pp. 261-274
- Peetre, J., On the theory of Lp,γ spaces (1969) J. Functional Analysis, 4, pp. 71-87
- Riveros, M.S., De La Torre, A., On the best ranges for Ap + and RHr + (2001) Czechoslovak Math. J., 51 (2-126), pp. 285-301
- De Rosa, L., Segovia, C., Weighted Hp spaces for one sided maximal functions (1994) Harmonic Analysis and Operator Theory, 189, pp. 161-183. , (Caracas), Contemp. Math., Amer. Math. Soc., Providence, RI
- De Rosa, L., Segovia, C., Dual spaces for one-sided weighted Hardy spaces (1997) Rev. Un. Mat. Argentina, 40 (3-4), pp. 49-71
- Sawyer, E., Weighted inequalities for the one-sided Hardy-Littlewood maximal functions (1986) Trans. Amer. Math. Soc., 297 (1), pp. 53-61
Citas:
---------- APA ----------
Ombrosi, S. & De Rosa, L. (2003) . Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces. Publicacions Matematiques, 47(1), 71-102.http://dx.doi.org/10.5565/PUBLMAT_47103_04
---------- CHICAGO ----------
Ombrosi, S., De Rosa, L. "Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces" . Publicacions Matematiques 47, no. 1 (2003) : 71-102.http://dx.doi.org/10.5565/PUBLMAT_47103_04
---------- MLA ----------
Ombrosi, S., De Rosa, L. "Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces" . Publicacions Matematiques, vol. 47, no. 1, 2003, pp. 71-102.http://dx.doi.org/10.5565/PUBLMAT_47103_04
---------- VANCOUVER ----------
Ombrosi, S., De Rosa, L. Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces. Publ. Mat. 2003;47(1):71-102.http://dx.doi.org/10.5565/PUBLMAT_47103_04
