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Let L be a generator of a semigroup satisfying the Gaussian upper bounds. Inthis paper, we study further a new BMO_L space associated with L which wasintroduced recently by Duong and Yan. We discuss applications of the new BMO_Lspaces in the theory of singular integration such as BMO_L estimates andinterpolation results for fractional powers, purely imaginary powers andspectral multipliers of self adjoint operators. We also demonstrate that thespace BMO_L might coincide with or might be essentially different from theclassical BMO space.

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