摘要
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 Calderon-Zygrnund 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.
基金
Project supported by the National Natural Science Foundation of China (No. 10271015)
the Program for New Century Excellent Talents in Universities of China (No. NCET-04-0142).