L^p-Logvinenko-Sereda sets and L^p-Carleson measures on compact manifolds

2025/06/28 by Wang, Xing, Xu, Xiangjin, Zhang, Cheng
#35P99 #58C35 #58C40 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2506.22759

Abstract

Marzo and Ortega-Cerdà gave geometric characterizations for L^p-Logvinenko-Sereda sets on the standard sphere for all 1≤ p<∞. Later, Ortega-Cerdà and Pridhnani further investigated L²-Logvinenko-Sereda sets and L²-Carleson measures on compact manifolds without boundary. In this paper, we characterize L^p-Logvinenko-Sereda sets and L^p-Carleson measures on compact manifolds with or without boundary for all 1 (2m)/(m-1). For the range p < (2m)/(m-1), we conjecture that L^p-Logvinenko-Sereda sets for eigenfunctions on the standard sphere S^m are characterized by the tubular geometric control condition and we provide some evidence. These results provide new progress on an open problem raised by Ortega-Cerdà and Pridhnani.

Citations

• Bernstein inequalities via the heat semigroup
• Observability properties of the homogeneous wave equation on a closed manifold
• Problems related to the concentration of eigenfunctions
• Boundedness of spectral multipliers of generalized Laplacians on compact\n manifolds with boundary
• Estimates for functions of the Laplacian on manifolds with bounded geometry
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Riemannian manifolds with maximal eigenfunction growth
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains

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• Some Carleson measures for the Hilbert-Hardy space of tube domains over\n symmetric cones
• Carleson measures for weighted Hardy-Sobolev spaces
• Carleson measures for Hilbert spaces of analytic functions on the complex half-plane