Author

Ji Li

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Preprint Oct 2026

Compactness and essential norms for two-weight fractional Riesz transforms on curves

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

Preprint Oct 2026

Two-weight T1 theorem for fractional Riesz transforms: one measure supported on a $C^{1,\mathrm{Dini}}$ curve

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

Preprint Aug 2026

Two-weight commutators for the Bessel Riesz transform with Andersen--Kerman weights

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

Preprint Sep 2026

Polynomial corners in finite fields beyond the distinct-degree case

We prove a quantitative polynomial Roth theorem for corners in $\mathbb F_p^2$ for arbitrary pairs of linearly independent polynomials. More precisely, given a positive integer $d$, there are constants $p_0$ and $C$ (depending only on $p$) so that for every $ p>p_0$, if polynomials \(\phi_1,\phi_2\in \mathbb \mathbb{...

Ji Li, Chun-Yen Shen, T. Truong et al. · 0 citations

Preprint Sep 2026

Commutators with two matrix weights

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

Preprint Aug 2026

On the endpoint estimate for discrete spherical average over sparse sequences

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