TY - JOUR
T1 - Borderline Weighted Estimates for Commutators of Fractional Integrals
AU - Wang , Zhidan
AU - Wu , Huoxiong
AU - Xue , Qingying
JO - Analysis in Theory and Applications
VL - 3
SP - 404
EP - 425
PY - 2021
DA - 2021/09
SN - 37
DO - http://doi.org/10.4208/ata.2021.lu80.08
UR - https://global-sci.org/intro/article_detail/ata/19881.html
KW - Commutators, fractional integrals, borderline weighted estimates, Fefferman-Stein inequality.
AB - <p style="text-align: justify;">Let $I_{\alpha,\vec{b}}$ be the multilinear commutators of the fractional integrals $I_{\alpha}$ with the symbol $\vec{b}=(b_1,&nbsp; \cdots,b_k&nbsp; )$. 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 $Osc_{\exp L^{s_i}}$.</p>