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Deng, Donggao; Duong, Xuan Thinh; Sikora, Adam; Yan, Lixin

Comparison of the classical BMO with the BMO spaces associated with operators and applications. (English) Zbl 1283.42036

Rev. Mat. Iberoam. 24, No. 1, 267-296 (2008).
Summary: Let \(L\) be a generator of a semigroup satisfying the Gaussian upper bounds. A new BMO\(_L\) space associated with \(L\) was recently introduced in [15] and [16]. We discuss applications of the new BMO\(_L\) spaces in the theory of singular integration. For example we obtain 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 BMO\(_L\) might coincide with or might be essentially different from the classical BMO space.

Cited in 20 Documents

MSC:

42B35 Function spaces arising in harmonic analysis
42B25 Maximal functions, Littlewood-Paley theory
47B38 Linear operators on function spaces (general)

Keywords:

BMO space; Hardy space; Dirichlet and Neumann Laplacians; semigroup; Gaussian bounds; fractional powers; purely imaginary powers; spectral multiplier
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\textit{D. Deng} et al., Rev. Mat. Iberoam. 24, No. 1, 267--296 (2008; Zbl 1283.42036)
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