We prove a compact two-weight $T1$ theorem for the $\alpha$-fractional Riesz vector, $0\leq\alpha<n$, when one measure is supported on a compact regular $C^{1,\mathrm{Dini}}$ curve $\Gamma$. The measures may have common point masses. Under the global boundedness assumptions, we give a two-sided estimate for the essenti...
Ji Li, Chun-Yen Shen, Chao-Jie Wen et al.· 0 citations
Let $0\leq\alpha<n$, and let $\sigma$ and $\omega$ be locally finite positive Borel measures on $\R^n$, possibly with common point masses. Suppose that one measure is supported on a compact regular $C^{1,\mathrm{Dini}}$ curve. We prove that the $\alpha$-fractional Riesz vector maps $L^2(\sigma)$ to $L^2(\omega)$ if and...
Ji Li, Chun-Yen Shen, Eric T. Sawyer 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
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