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

Donggao Deng·Xuan Thinh Duong·Adam Sikora·Lixin Yan
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Abstract

Let L be a generator of a semigroup satisfying the Gaussian upper bounds. In this paper, we study further a new BMO_L space associated with L which was introduced recently by Duong and Yan. We discuss applications of the new BMO_L spaces in the theory of singular integration such as 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.

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Donggao Deng, Xuan Thinh Duong, Adam Sikora, Lixin Yan. 2006-09-15. Comparison of the classical BMO with the BMO spaces associated with operators and applications. https://arxiv.org/abs/math/0609454

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