Borderline Weighted Estimates for Commutators of Fractional Integrals (Analysis in Theory and Applications, 2022)
Let $I_{α,\vec{b}}$ be the multilinear commutators of the fractional integrals $I_{α}$ with the symbol $\vec{b}=(b_1, …,b_k )$. We show that the constant of borderline weighted estimates for $I_{α}$ is $\frac{1}{ε}$, and for $I_{α,{\vec{b}}}$ is $\frac{1}{ε^{k+1}}$ with each $b_i$ belongs to the Orlicz space $Osc_{\exp L^{s_i}}$.
Keywords: Commutators; fractional integrals; borderline weighted estimates; Fefferman-Stein inequality.