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April, 2008 Comparison of the classical BMO with the BMO spaces associated with operators and applications
Donggao Deng , Xuan Thinh Duong , Adam Sikora , Lixin Yan
Rev. Mat. Iberoamericana 24(1): 267-296 (April, 2008).

Abstract

Let $L$ be a generator of a semigroup satisfying the Gaussian upper bounds. A new ${\rm BMO}_L$ space associated with $L$ 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 ${\rm BMO}_L$ spaces in the theory of singular integration. For example we obtain ${\rm BMO}_L$ estimates and interpolation results for fractional powers, purely imaginary powers and spectral multipliers of self adjoint operators. We also demonstrate that the space ${\rm BMO}_L$ might coincide with or might be essentially different from the classical BMO space.

Citation

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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. Iberoamericana 24 (1) 267 - 296, April, 2008.

Information

Published: April, 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1283.42036
MathSciNet: MR2435973

Subjects:
Primary: 42B25, 42B35, 47B38

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.24 • No. 1 • April, 2008
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