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Commutators and BMO: from Calderón–Zygmund operators to singular integrals with non-smooth kernels, I & II.

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系列学术活动之(69)

题    目:



Commutators and BMO: from Calderón–Zygmund operators to singular integrals with non-smooth kernels, I & II.


摘    要:

It is well-known that the commutator of Riesz transform (Hilbert transform in dimension 1) and a symbol  is bounded on  if and only if  is in the  space  Inspired by this result, it is natural to ask whether it holds for commutator of some other Calderón–Zygmund operators. We provide confirmative answers for certain Calderón–Zygmund operators, such as the Riesz transforms associated with Neumann Laplacian, Bessel operators, Riesz transforms on Stratified Lie groups, et al. The proof of lower bound is inspired by methods from Uchiyama and Lerner-Ombrossi-Rivera-Ríos. We further developed and adapted to the study of commutator in the setting of singular integrals with non-smooth kernels, such as the Cauchy type integrals for domains in with minimal smoothness (studied by Lanzani–Stein), which are beyond the standard frame of Calderón–Zygmund operators.


报 告 人:

李冀,澳大利亚Macquarie大学(麦考瑞大学)数学系Senior Lecturer

时    间:

2018122515:00

地    点:

科技大楼617





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