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Generalized Hardy Spaces 被引量：3

Generalized Hardy Spaces
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摘要 Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting. Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting.
作者 Alexandre ALMEIDA António M.CAETANO
机构地区 Departamento de Matemática
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第9期1673-1692,共20页 数学学报（英文版）
基金 Supported by the Research Unit Matemática e Aplicac■s (UIMA) of University of Aveiro, Portugal
关键词 Generalized Hardy spaces maximal functions Poisson kernel interpolation with function parameter Riesz potentials singular integrals Generalized Hardy spaces, maximal functions, Poisson kernel, interpolation with function parameter, Riesz potentials, singular integrals
分类号 O177 [理学—基础数学]
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参考文献27

  • 1Stein, E. M., Weiss, G.: On the theory of harmonic functions of several variables, I, The theory of Hp spaces. Acta Math., 103, 25-62 (1960).
  • 2Fefferman, C., Stein, E. M.: Hp spaces of several variables. Acta Math., 129, 137-193 (1972).
  • 3Coifman, R. R.: A real variable characterization of Hp. Studia Math., 51, 269-274 (1974).
  • 4Latter, R.: A decomposition of Hp(R^n) in terms of atoms. Studia Math., 62, 93-101 (1978).
  • 5Stein, E. M.: Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Prince- ton University Press, Princeton, 1993.
  • 6Lu, S.: Four lectures on real Hp spaces, World Scientific, Singapore, 1995.
  • 7Garcfa-Cuerva, J.: Weighted Hp spaces. Dissertationes Math., 162, 1-63 (1979).
  • 8Fefferman, C., Riviere, N. M., Sagher, Y.: Interpolation between HP-spaces: the real method. Trans. Amer. Math. Soc. 191, 75-81 (1974).
  • 9Abu-Shammala, W., Torchinsky, A.: The Hardy-Lorentz spaces H^Pq(R^n). Studia Math., 182, 283-294 (2007).
  • 10Coifman, R. R., Weiss, G.: Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc., 83, 569-645 (1977).

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Acta Mathematica Sinica,English Series
2010年 第9期

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