Comparison of the classical BMO with the BMO spaces associated with operators and applications
Analysis of PDEs
2007-05-23 v1 Functional Analysis
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.
Cite
@article{arxiv.math/0609454,
title = {Comparison of the classical BMO with the BMO spaces associated with operators and applications},
author = {Donggao Deng and Xuan Thinh Duong and Adam Sikora and Lixin Yan},
journal= {arXiv preprint arXiv:math/0609454},
year = {2007}
}