Multilinear commutators of singular integrals with non doubling measures
Multilinear commutators of singular integrals with non doubling measures
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DOI：
10.1007/s00020-003-1251-y
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发表时间：
2005-02-01
影响因子：
0.8
通讯作者：
Yang, DC
中科院分区：
文献类型：
--
作者：
Hu, G;Meng, Y;Yang, DC
设μ是R-d上的Radon测度，它可以是非加倍的。μ必须满足的唯一条件是μ（B（x，r））小于或等于Cr-n，对于所有x是R-d的元素，r > 0，并且对于某个固定的0 < n小于或等于d。本文在此假设下，讨论了L-P（mu）-有界性对于由Calderon-Zygmund奇异积分与RBMO（μ）函数或Osc（exp）L（T）（μ）函数生成的多线性算子，当r大于或等于1时，建立了（1其中Osc（exp）L（T）（mu）是Orlicz型空间，当r = 1时满足Osc（exp）L-T（mu）= RBMO（mu），当r > 1时满足Osc（exp）L（T）（mu）是RBMO（mu）的子集。
Let mu be a Radon measure on R-d which may be non-doubling. The only condition that mu must satisfy is mu(B(x, r)) less than or equal to Cr-n for all x is an element of R-d, r > 0 and for some fixed 0 < n less than or equal to d. In this paper, under this assumption, the L-P(mu)-boundedness (1 < p < infinity) and certain weak type endpoint estimate are established for multilinear commutators, which are generated by Calderon-Zygmund singular integrals with RBMO(mu) functions or with Osc(exp)L(T) (mu) functions for r greater than or equal to 1, where Osc(exp)L(T)(mu) is a space of Orlicz type satisfying that Osc(exp) L-T (mu) = RBMO(mu) if r = 1 and Osc(exp)L(T)(mu) subset of RBMO(mu) if r > 1.