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Product of Functions in BMO and H1 in Non-homogeneous Spaces

Product of Functions in BMO and H1 in Non-homogeneous Spaces
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摘要 Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular BMO and the atomic block -~1 in the sense of distribution, and show that this product may be split into two parts, one in L1 and the other in some Hardy-Orlicz space. Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular BMO and the atomic block -~1 in the sense of distribution, and show that this product may be split into two parts, one in L1 and the other in some Hardy-Orlicz space.
作者 Justin FEUTO
机构地区 Universitd de Cocody
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第8期1535-1546,共12页 数学学报（英文版）
关键词 Local Hardy space local BMO space atomic block BLOCK non-doubling measure Hardy- Orlicz space Local Hardy space, local BMO space, atomic block, block, non-doubling measure, Hardy- Orlicz space
分类号 O177.3 [理学—基础数学] TU746.3 [建筑科学—建筑技术科学]
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参考文献15

  • 1Bonami, A., Iwaniec, T., Jones, P., et al.: On the product of Functions in BMO and 7-/1. Ann. Inst. Fourier, Grenoble, 57'(5), 1405-1439 (2007).
  • 2Bonami, A., Feuto, J.: Products of functions in Hardy and Lipschitz or BMO spaces. Recent Developments in Real and Harmonic Analysis: In Honor of Carlos Segovia, Applied and Numerical Harmonic Analysis, 2009, 57-71, DOI: 10.1007/978-0-8176-4588-5-4.
  • 3Golberg, D.: A local version of Hardy spaces. Duke Math. J., 46, 27 -42 (1979).
  • 4Wiener, N.: On the representation of functions by trigonometrical integrals. Math. Z., 24, 575-616 (1926).
  • 5Feuto, J.: Products of functions in BMO and H1 spaces on spaces of homogeneous type. J. Math. Anal. Appl., 359, 610-620 (2009).
  • 6Mateu, J., Mattila, P., Nicolau, A., et al.: BMO for nondoubling measures. Duke Math. J., 102(3), 533-565 (2000).
  • 7Tolsa, X.: BMO, H1, and Calderon-Zygmund operators for non-doubling measures. Math. Ann., 319, 89-149 (2001).
  • 8Tolsa, X.: The space H1 for non-doubling measures in terms of a grand maximal operator. Trans. Amer. Math. Soc., 335, 315-348 (2003).
  • 9Yang, D.: Local Hardy and BMO spaces on nonhomogeneous spaces. J. Aust. Math. Soc., 79, 149-182 (2005).
  • 10Hu, G., Liang, S.: Another characterization of the Hardy space with nondoubling measures. Math. Nachr., 279(16), 1797-1807 (2006).
Acta Mathematica Sinica,English Series
2011年 第8期

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