Anal. Theory Appl., 37 (2021), pp. 404-425.
Published online: 2021-09
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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 $Osc_{\exp L^{s_i}}$.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2021.lu80.08}, url = {http://global-sci.org/intro/article_detail/ata/19881.html} }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 $Osc_{\exp L^{s_i}}$.