A geometry-independent endpoint estimate for the Littlewood--Paley $g$-function generated by the Poisson semigroup
Year: 2026
Type: preprint
Abstract: 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 $L^2((0,\infty),dt/t)$.
Source: arXiv (Cornell University)
Authors: Li, Bo, Li, Ji, Li, Jinxia
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3593533857, G6915249523, G8847952484
OpenAlex ID: W7222558277