Abstract
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderón-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H 1(μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measure μ is the d-dimensional Lebesgue measure.
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* Project supported by the National Natural Science Foundation of China (No. 10271015) and the Program for New Century Excellent Talents in Universities of China (No. NCET-04-0142).
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Fu, X., Meng, Y. & Yang, D. Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces*. Chin. Ann. Math. Ser. B 28, 67–80 (2007). https://doi.org/10.1007/s11401-005-0355-x
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DOI: https://doi.org/10.1007/s11401-005-0355-x