JournalsrmiVol. 24, No. 1pp. 267–296

Comparison of the classical BMO with the BMO spaces associated with operators and applications

  • Donggao Deng

    Zhongshan University, Guangzhou, Guangdong, China
  • Xuan Thinh Duong

    Macquarie University, Sydney, Australia
  • Adam Sikora

    Macquarie University, Sydney, Australia
  • Lixin Yan

    Zhongshan University, Guangzhou, China
Comparison of the classical BMO with the BMO spaces associated with operators and applications cover
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Abstract

Let LL be a generator of a semigroup satisfying the Gaussian upper bounds. A new BMOL{\rm BMO}_L space associated with LL was recently introduced in [Duong, X. T. and Yan, L.: {New function spaces of BMO type, the John-Nirenberg inequality, interpolation and applications}. \textit{Comm. Pure Appl. Math.} {\bf 58} (2005), 1375-1420] and [Duong, X. T. and Yan, L.: {Duality of Hardy and BMO spaces associated with operators with heat kernels bounds}. \textit{J. Amer. Math. Soc.} {\bf 18} (2005), 943-973]. We discuss applications of the new BMOL{\rm BMO}_L spaces in the theory of singular integration. For example we obtain BMOL{\rm BMO}_L estimates and interpolation results for fractional powers, purely imaginary powers and spectral multipliers of self adjoint operators. We also demonstrate that the space BMOL{\rm BMO}_L might coincide with or might be essentially different from the classical BMO space.

Cite this article

Donggao Deng, Xuan Thinh Duong, Adam Sikora, Lixin Yan, Comparison of the classical BMO with the BMO spaces associated with operators and applications. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 267–296

DOI 10.4171/RMI/536