带非光滑核的多线性Marcinkiewicz积分的加权界
Weighted Bounds for Multilinear Marcinkiewicz Integrals with Nonsmooth Kernel
我们引入了带非光滑核的多线性Marcinkiewicz积分算子.设p1,…,pm∈(1,∞)和p∈(0,+∞)满足1/p1+…+1/pm=1/p,记P=(p1,…,pm),又设向量权ω=(ω1,…,ωm)∈ AP和νω=∏k=1mωkp/pk,得到了Marcinkiewicz积分算子从Lp1(ω1)×…×Lpm(ωm)到Lp(νω)的常数界.
We introduce the multilinear Marcinkiewicz integrals with nonsmooth kernel and get their the weighted bounds from Lp1(ω1)×…×Lpm(ωm) to Lp(νω) with p1, …, pm ∈ (1, ∞), 1/p1 + … + 1/pm=1/p and ω=(ω1, …, ωm) a multiple AP weights, where P=(p1, …, pm) and νω=∏k=1m ωkp/pk.
多线性Marcinkiewicz积分 / 非光滑核 / 多权 {{custom_keyword}} /
multilinear Marcinkiewicz integrals / non-smooth kernel / multiple weight {{custom_keyword}} /
[1] Chen J., Hu G., Weighted vector-valued bounds for a class of multilinear singular integral operators and applications, arXiv:1606.04768v3.
[2] Duong X., Grafakos L., Yan L., Multilinear operators with non-smooth kernels and commutators of singular integrals, Trans. Amer. Math. Soc., 2010, 362:2089-2113.
[3] Fefferman C., Stein E. M., Some maximal inequalities, Amer. J. Math., 1971, 93:107-115.
[4] Hytönen T., Lacey M., Pérez C., Sharp weighted bounds for the q-variation of singular integrals, Bull. Lond. Math. Soc., 2013, 45:529-540.
[5] Lerner A., On pointwise estimate involving spares operator, New York J. Math., 2016, 22:341-349.
[6] Lerner A., Obmrosi S., Rivera-Rios I., On pointwise and weighted estimates for commutators of Calderón-Zygmund operators, arXiv:1604.01334.
[7] Lerner A., Ombrosi S., Pérez C., et al., New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory, Adv. Math., 2009, 220:1222-1264.
[8] Li K., Sparse domination theorem for multilinear singular integral operators with Lr-Hörmander condition, arXiv:1606.03952.
[9] Li K., Moen K., Sun W., The sharp weighted bound for multilinear maximal functions and Calderón-Zygmund operators, J. Fourier Anal. Appl., 2014, 20:751-765.
湖北省教育厅青年人才资助项目(Q20162504)
/
〈 | 〉 |