Borderline Weighted Estimates for Commutators of Fractional Integrals
Zhidan WangSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems Ministry of Education, Beijing 100875, ChinaHuoxiong WuSchool of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, ChinaQingying XueSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems Ministry of Education, Beijing 100875, China
2021en
ABI
Abstract
Let $I_{\alpha,\vec{b}}$ be the multilinear commutators of the fractional integrals $I_{\alpha}$ with the symbol $\vec{b}=(b_1, \cdots,b_k )$. We show that the constant of borderline weighted estimates for $I_{\alpha}$ is $\frac{1}{{\varepsilon}}$, and for $I_{\alpha,{\vec{b}}}$ is $\frac{1}{{\varepsilon}^{k+1}}$ with each $b_i$ belongs to the Orlicz space $Osc_{\exp L^{s_i}}$.
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