Comparison of the classical BMO with the BMO spaces associated with operators and applications
Donggao Deng, Xuan Thinh Duong, Adam Sikora, Lixin Yan
Abstract
Let L be a generator of a semigroup satisfying the Gaussian upper bounds. In this paper, we study further a new BMOL space associated with L which was introduced recently by Duong and Yan. We discuss applications of the new BMOL spaces in the theory of singular integration such as BMOL estimates and interpolation results for fractional powers, purely imaginary powers and spectral multipliers of self adjoint operators. We also demonstrate that the space BMOL might coincide with or might be essentially different from the classical BMO space.
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