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Weighted Weak-type Estimates for Multilinear Commutators of Fractional Integrals on Spaces of Homogeneous Type 被引量：5

Weighted Weak-type Estimates for Multilinear Commutators of Fractional Integrals on Spaces of Homogeneous Type
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摘要 We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself. We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.
作者 Osvaldo GOROSITO Gladis PRADOLINI Oscar SALINAS
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第10期1813-1826,共14页 数学学报（英文版）
基金 Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina Universidad Nacional del Litoral
关键词 COMMUTATORS fractional integral operator multilinear operators commutators, fractional integral operator, multilinear operators
分类号 O177.6 [理学—基础数学]
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参考文献23

  • 1Chanillo, S.: A note on commutators. Indiana Univ. Math. J., 31, 7-16 (1982).
  • 2Segovia, C., Torrea, J. L.: Weighted inequalities for commutators of fractional and singular integrals. Publ. Matematiques, 35, 209--235 (1991).
  • 3Bramanti, M., Cerutti, M.C.: Commutators of singular integrals and fractional integrals on homogeneous spaces, Harmonic Analysis and Operator Theory, (Caracas 1994), (Providence, RI). Conterap. Math., A.M.S., 189, 81-94 (1995).
  • 4Betancor, J.: A commutator theorem for fractional integrals in spaces of homogeneous type. Inter'nat. J. Math. & Math. Sci., 24(6), 403-418 (2000).
  • 5Harboure, E., Segovia, C., Torrea, J. L.: Boundedness of commutators of fractional and singular integrals for the extreme values of p. Illinois J. of Math., 41(4), 676-700 (1997).
  • 6Perez, C., Trujillo-Conzalez, R.: Sharp weighted estimates for multilinear commutators. J. London Math. Soc., 65(2), 672-692 (2002).
  • 7Maocias, R., Segovia, C.: Lipschitz functions on spaces of homogeneous type. Adv. Math., 33, 257-270 (1979).
  • 8Bernardis, A., Salinas, O.: Two-weighted inequalities for certain maximal fractional operators on spaces of homogeneous type. Revista de la Union Matemdtica Argentina, 41(3), 61-75 (1999).
  • 9Cruz Uribe, D., Fiorenza, A.: Endpoint estimates and weighted norm inequalities for commutators of fractional integrals. Publ. Mat., 47, 103-131 (2003).
  • 10Ding, Y., Lu, S. Z, Zhang, P.: Weak estimates for commutators of fractional integral operators. Science in China (Series A), 44(7), 877-888 (2001).

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Acta Mathematica Sinica,English Series
2007年 第10期

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