Let $\alpha>-1/2$, $\alpha\ne0$, and let $$ \Delta_\alpha=-\frac{d^2}{dx^2}-\frac{2\alpha}{x}\frac{d}{dx} $$ be the Bessel operator on $\mathbb R_+=(0,\infty)$. We characterize boundedness and compactness of commutators of $R_\alpha=\frac{d}{dx}\Delta_\alpha^{-1/2}$ on the Andersen--Kerman two-weight setting. For $1<p<...
Ji Li, Chong-Wei Liang, Chao-Jie Wen et al.· 0 citations
Let $U,V$ be matrix $\mathcal A_p$ weights, $1<p<\infty$, and let $B$ be a matrix-valued function. For Calder\'on--Zygmund operators $T$ with scalar standard kernels, we characterize boundedness and compactness of $[M_B,T\otimes I_m]:L^p(U)\to L^p(V)$ by two-matrix BMO and vanishing oscillation conditions. The converse...
Ji Li, Chong-Wei Liang, Chun-Yen Shen et al.· 2 citations· ⚡1
For $0<d\leq1/4$, let $\mathcal{C}(d)$ be the four-corner Cantor set with Hausdorff dimension $s_d=\log 4/\log(1/d)$. Peres, Simon, and Solomyak, as well as Mattila, asked for which $d$ the measure $\Hau^{s_d}(p_\theta(\mathcal{C}(d)))$ is positive for almost every direction $\theta$. It was open for the range $1/9\leq...
Let $d\ge5$, and let $A_\lambda$ denote the normalized discrete spherical average on $\mathbb{Z}^d$ with squared radius $\lambda$. For a strictly increasing sequence $(\mu_k)$ of positive integers, set $\lambda_k=\mu_k!$ and consider the lacunary maximal operator $A_\star f:=\sup_k|A_{\lambda_k}f|$. For each fixed $\ga...
Sanghyuk Lee, Ji Li, Chong-Wei Liang et al.· 0 citations
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