Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces*
Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces*
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DOI：
10.1007/s11401-005-0355-x
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发表时间：
2006-01
期刊：
影响因子：
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通讯作者：
Xi Fu;Y. Meng;Dachun Yang
中科院分区：
文献类型：
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作者：
Xi Fu;Y. Meng;Dachun Yang
摘要：在假设底层测度是仅满足一定增长条件的非负氡测度的情况下，作者证明了对于一类具有Lipschitz函数的换向器（包括由Calderón-Zygmund算子生成的换向器和Lipschitz函数为例），它们在Lebesgue空间或Hardy空间H1(μ)中的有界性等价于它们满足的某些端点估计。即使底层测度μ是 d 维勒贝格测度，这个结果也是新的。
AbstractUnder 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 spaceH1(μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measureμis thed-dimensional Lebesgue measure.