Multilinear operators with non-smooth kernels and commutators of singular integrals
Multilinear operators with non-smooth kernels and commutators of singular integrals
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DOI：
10.1090/s0002-9947-09-04867-3
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发表时间：
2009-10
影响因子：
1.3
通讯作者：
X. Duong;Loukas Grafakos;Lixin Yan
中科院分区：
文献类型：
--
作者：
X. Duong;Loukas Grafakos;Lixin Yan
我们得到了多线性奇异积分算子的端点估计，其核所满足的正则性条件比标准的卡尔德隆 - 齐格蒙德核的条件要弱得多。因此，我们推导出了卡尔德隆的\(m\)阶交换子从\(L^1\times\cdots\times L^1\)到弱\(L^{1/m}\)的估计。我们的结果重现了\(m = 1,2\)时的已知估计，但对于\(m>3\)是新的。我们还探讨了二阶高维交换子与双线性希尔伯特变换之间的联系，并为前者推导出了一些新的非对角估计。
We obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the standard Calder6n-Zygmund kernels. As a consequence, we deduce endpoint L 1 × ··· x L 1 to weak L 1/m estimates for the mth-order commutator of Calderon. Our results reproduce known estimates for m = 1, 2 but are new for m > 3. We also explore connections between the 2nd-order higher-dimensional commutator and the bilinear Hilbert transform and deduce some new off-diagonal estimates for the former.