arXiv subjects

Jinxia Li

Publications and source records attributed to Jinxia Li.

2 recordsLinked to original sources

arXiv2026

A geometry-independent endpoint estimate for the Littlewood--Paley $g$-function generated by the Poisson semigroup

We prove a weak $(1,1)$ estimate for the full Poisson Littlewood--Paley $g$-function on every complete Riemannian manifold without boundary, with an explicit universal constant approximately equal to $3.33606$. The estimate requires no curvature restriction, volume doubling, heat kernel bound, or stochastic completeness. The proof combines a precise Poisson maximal inequality with a convex entropy identity; local elliptic regularity identifies the extension to arbitrary real $L^1$ data. As an application, we obtain weak $(1,1)$ estimates for certain spectral multipliers represented by Poisson time derivatives with coefficients in $L^2((0,\infty),dt/t)$.

math.CA↗

arXiv2020

Variable Anisotropic Singular Integral Operators

We introduce the class of variable anisotropic singular integral operators associated to a continuous multi-level ellipsoid cover $Θ$ of $\mathbb{R}^n$ introduced by Dahmen, Dekel, and Petrushev \cite{ddp}. This is an extension of the classical isotropic singular integral operators on $\mathbb{R}^n$ of arbitrary smoothness and their anisotropic analogues for general expansive matrices introduced by the first author \cite{b}. We establish the boundedness of variable anisotropic singular integral operators $T$ on the Hardy spaces with pointwise variable anisotropy $H^p(Θ)$, which were developed by Dekel, Petrushev, and Weissblat \cite{dpw}. In contrast with the general theory of Hardy spaces on spaces of homogenous type, our results work in the full range $0<p\leq 1$.

math.FA↗