Artículo
Riveros, M.S.; De Rosa, L.; De La Torre, A. "Sufficient conditions for one-sided operators" (2000) Journal of Fourier Analysis and Applications. 6(6):607-621
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Abstract:
In this article we give sufficient conditions on a pair of weights (w, v) for some one-sided operators to be bounded from Lp(vp) to Lp(wp). The operators we deal with include the one-sided fractional maximal operator and the one-sided singular integrals. For the first operator, necessary and sufficient conditions are known (see [8, 6]). These conditions usually amount to checking the boundedness of the operator on functions that are powers of the weights and are hard to check. Our conditions are of Ap type and are therefore easy to verify. Similar results for two-sided operators were obtained by C. Pérez in [9] and [10]. © 2000 Birkhäuser Boston. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | Sufficient conditions for one-sided operators |
| Autor: | Riveros, M.S.; De Rosa, L.; De La Torre, A. |
| Filiación: | Fa.MAF Universidad Nacional de Córdoba, 5000 Córdoba, Argentina Dpto. de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain |
| Palabras clave: | Banach function spaces; Maximal fractional integrals; One-sided weights; Singular integrals |
| Año: | 2000 |
| Volumen: | 6 |
| Número: | 6 |
| Página de inicio: | 607 |
| Página de fin: | 621 |
| DOI: | http://dx.doi.org/10.1007/BF02510698 |
| Título revista: | Journal of Fourier Analysis and Applications |
| Título revista abreviado: | J. Fourier Anal. Appl. |
| ISSN: | 10695869 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v6_n6_p607_Riveros |
Referencias:
- Andersen, K.F., Sawyer, E., Weighted norm inequalities for Riemann-Liouville and Weyl fractional integral operators (1988) Trans. Am. Math. Soc., 308, pp. 547-557
- Aimar, H., Forzani, L., Martin-Reyes, F.J., On weighted inequalities for one-sided singular integrals (1997) Proc. Am. Math. Soc, 125, pp. 2057-2064
- Bliendtner, J., Loeb, P., A reduction technique for limit theorems in analysis and probability theory (1992) Ark. Mat., 30, pp. 25-43
- Córdoba, A., Fefferman, C., A weighted norm inequality for singular integrals (1976) Studia Math., 57, pp. 97-101
- Garcia Cuerva, J., Rubio De Francia, J.L., Weighted norm inequalities and related topics (1985) North-Holland Math. Studies, 116. , North-Holland, Amsterdam
- Lorente, M., De La Torre, A., Weighted inequalities for some one-sided operators (1996) Proc. Am. Math. Soc, 124 (3), pp. 839-848
- Martín-Reyes, F.J., Ortega, P., De La Torre, A., Weighted inequalities for one-sided maximal functions (1990) Trans. Am. Math. Soc, 319 (2), pp. 517-534
- Martín-Reyes, F.J., De La Torre, A., Two weight inequalities for fractional one-sided maximal operators (1993) Proc. Am. Math. Soc, 117 (2), pp. 483-489
- Pérez, C., On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted Lp-spaces with different weights (1995) Proc. London Math. Soc., 71 (3), pp. 135-157
- Pérez, C., Weighted norm inequalities for singular integral operators (1994) J. London Math. Soc., 49, pp. 296-308
- Pérez, C., Two weighted inequalities for potential and fractional type maximal operators (1994) Indiana Univ. Math., 43, pp. 1-28
- Sawyer, E., A characterization of a two-weighted norm inequality for maximal operators (1982) Studia Math., 75, pp. 1-11
Citas:
---------- APA ----------
Riveros, M.S., De Rosa, L. & De La Torre, A. (2000) . Sufficient conditions for one-sided operators. Journal of Fourier Analysis and Applications, 6(6), 607-621.http://dx.doi.org/10.1007/BF02510698
---------- CHICAGO ----------
Riveros, M.S., De Rosa, L., De La Torre, A. "Sufficient conditions for one-sided operators" . Journal of Fourier Analysis and Applications 6, no. 6 (2000) : 607-621.http://dx.doi.org/10.1007/BF02510698
---------- MLA ----------
Riveros, M.S., De Rosa, L., De La Torre, A. "Sufficient conditions for one-sided operators" . Journal of Fourier Analysis and Applications, vol. 6, no. 6, 2000, pp. 607-621.http://dx.doi.org/10.1007/BF02510698
---------- VANCOUVER ----------
Riveros, M.S., De Rosa, L., De La Torre, A. Sufficient conditions for one-sided operators. J. Fourier Anal. Appl. 2000;6(6):607-621.http://dx.doi.org/10.1007/BF02510698
