Weighted inequalities for generalized fractional operators

• Autores: María Silvina Riveros
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 49, Nº. 2, 2008, págs. 29-38
• Idioma: inglés
• Enlaces
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• Resumen

  • In this note we present weighted Coifman type estimates, and two-weight estimates of strong and weak type for general fractional operators. We give applications to fractional operators given by an homogeneous function, and by a Fourier multiplier. The complete proofs of these results appear in the work [5] done jointly with Ana L. Bernardis and María Lorente.

• Referencias bibliográficas
  • Andersen, K. F., Sawyer, E. T.. (1988). Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators. Trans....
  • Bernardis, A.L., Lorente, M.. Sharp two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operator.
  • Bernardis, A.L., Lorente, M., Martín-Reyes, F.J., Martínez, M.T., de la Torre, A., Torrea, J.L.. (2006). Differential transforms in weighted...
  • Bernardis, A.L., Lorente, M., Pradolini, G., Riveros, M.S.. Composition of fractional Orlicz maximal operators and -weights on spaces of homogeneous...
  • Bernardis, A.L., Lorente, M., Riveros, M.S.. On Weighted inequalities for generalized fractional integrals operators.
  • Carro, M.J., Pérez, C., Soria, F., Soria, J.. (2005). Maximal functions and the control of weighted inequalities for the fractional integral...
  • Chanillo, S., Watson, D.K., Wheeden, R.L.. (1993). Some integral and maximal operators related to starlike sets. Studia Math.. 107. 223-255
  • Coifman, R.. (1972). Distribution function inequalities for singular integrals. Proc. Acad. Sci. U.S.A.. 69. 2838-2839
  • Ding, Y.. (1997). Weak type bounds for a class of rough operators with power weights. Proc. Amer. Math. Soc.. 125. 2939-2942
  • Ding, Y., Lu, S.. (1998). Weighted norm inequalities for fractional integral operators with rough kernel. Can. J. Math.. 50. 29-39
  • Jones, R.L., Rosenblatt, J.. (2002). Differential and ergodic transform. Math. Ann.. 323. 525-546
  • Kurtz, D.S.. (1979). Sharp function estimates for fractional integrals and related operators. Trans. Amer. Math. Soc.. 255. 343-362
  • Kurtz, D.S., Wheeden, R.L.. (1990). Results on weighted norm inequalities for multipliers. J. Austral. Math. Soc. A. 49. 129-137
  • Lorente, M., Martell, J.M., Riveros, M.S., de la Torre, A.. (2008). Generalized Hörmander's condition, commutators and weights. J. Math....
  • Lorente, M., Martell, J.M., Pérez, C., Riveros, M.S.. (2007). Generalized Hörmander's conditions and weighted endpoint estimates.
  • Lorente, M., Riveros, M.S., de la Torre, A.. (2005). Weighted estimates for singular integral operators satisfying Hörmander's conditions...
  • Martín-Reyes, F.J., de la Torre, A.. (1994). One Sided BMO Spaces. J. London Math. Soc. 2. 49. 529-542
  • Martín-Reyes, F.J., Ortega, P., de la Torre, A.. (1990). Weighted inequalities for one-sided maximal functions. Trans. Amer. Math. Soc.. 319....
  • Muckenhoupt, B.. (1972). Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc.. 165. 207-226
  • Muckenhoupt, B., Wheeden, R. L.. (1974). Weighted norm inequalities for fractional integrals. Trans. Amer. Math. Soc.. 192. 261-274
  • O'Neil, R.. (1963). Fractional integration in Orlicz spaces. Trans. Amer. Math. Soc.. 115. 300-328
  • Pérez, C.. (1994). Weighted norm inequalities for singular integral operators. J. London Math. Soc.. 49. 296-308
  • Pérez, C.. (1995). Sharp -weighted Sobolev inequalities. Ann. Inst. Fourier (Grenoble). 45. 809-824
  • Rao, M., Ren, Z.D.. (1991). Theory of Orlicz spaces. Marcel Dekker. New York.
  • Rubio de Francia, J.L., Ruiz, F.J., Torrea, J. L.. (1986). Calderón-Zygmund theory for vector-valued functions. Adv. in Math.. 62. 7-48
  • Sawyer, E.. (1986). Weighted inequalities for the one-sided Hardy-Littlewood maximal functions. Trans. Amer. Math. Soc.. 297. 53-61
  • Segovia, C., Torrea, J.L.. (1993). Higher order commutators for vector-valued Calderón-Zygnund operators. Trans. Amer. Math. Soc.. 336. 537-556