PreprintarXiv licencearXiv
A geometry-independent endpoint estimate for the Littlewood--Paley g-function generated by the Poisson semigroup
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 L1 data. As an application, we obtain weak (1,1) estimates for certain spectral multipliers represented by Poisson time derivatives with coefficients in L2((0,∞),dt/t).
Related
- Littlewood--Paley operators and semigroup maximal operators on CMO spaces associated to Schödinger operators
- Sparse Kahane--Salem--Zygmund Forms and Weighted Hardy--Littlewood Inequalities Across the Critical Endpoint
- The semigroup generated by linear fractional divergence form operators in Lp(ℝN): the constant coefficient case
- Betti Sequences of Four-Generated Non-Almost-Symmetric Nearly Gorenstein Numerical Semigroup Rings
- Geometry of three--generated ideals in the plane
BibTeX
@misc{li2026geometryindependent,
title = {{A geometry-independent endpoint estimate for the Littlewood--Paley $g$-function generated by the Poisson semigroup}},
author = {Bo Li and Ji Li and Jinxia Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21847},
eprint = {2610.21847},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21847},
}
RIS
TY - UNPB
TI - A geometry-independent endpoint estimate for the Littlewood--Paley g-function generated by the Poisson semigroup
AU - Bo Li
AU - Ji Li
AU - Jinxia Li
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21847
UR - https://arxiv.org/abs/2610.21847
AB - 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,∞),dt/t).
ER -