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

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

2006-09-15

arxiv.org/abs/math/0609454v1

Mathematics

Analysis of PDEs

Scientific paper

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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