2025/02/18 by Stefano Meda, Stefano Pigola, Meda, Stefano +5
Mathematics · #42B25 #53C20 #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2502.13109
openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the Lp boundedness of the centred and the uncentred Hardy--Littlewood maximal operators on certain Riemannian manifolds with bounded geometry. Our results complement those of various authors. We show that, under mild assumptions, Lp estimates for the centred operator are ``stable'' under conformal changes of the metric, and prove sharp~Lp estimates for the centred operator on Riemannian models with pinched negative scalar curvature. Furthermore, we prove that the centred operator is of weak type (1,1) on the connected sum of two space forms with negative curvature, whereas the uncentred operator is, perhaps surprisingly, bounded only on L^∞. We also prove that if two locally doubling geodesic metric measure spaces enjoying the uniform ball size condition are strictly quasi-isometric, then they share the same boundedness properties for both the centred and the uncentred maximal operator. Finally, we discuss some Lp mapping properties for the centred operator on a specific Riemannian surface introduced by Strömberg, providing new interesting results.