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• W2029386867 abstract "Let X be a compact, connected, Riemannian manifold (without boundary), ρ be the geodesic distance on X, μ be a probability measure on X, and {ϕk} be an orthonormal (with respect to μ) system of continuous functions, ϕ0(x)=1 for all x∈X, {ℓk}k=0∞ be a nondecreasing sequence of real numbers with ℓ0=1, ℓk↑∞ as k→∞, ΠL:=span{ϕj:ℓj≤L}, L≥0. We describe conditions to ensure an equivalence between the Lp norms of elements of ΠL with their suitably discretized versions. We also give intrinsic criteria to determine if any system of weights and nodes allows such inequalities. The results are stated in a very general form, applicable for example, when the discretization of the integrals is based on weighted averages of the elements of ΠL on geodesic balls rather than point evaluations." @default.
• W2029386867 created "2016-06-24" @default.
• W2029386867 creator A5056481363 @default.
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• W2029386867 date "2011-12-01" @default.
• W2029386867 modified "2023-10-18" @default.
• W2029386867 title "Marcinkiewicz–Zygmund measures on manifolds" @default.
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• W2029386867 doi "https://doi.org/10.1016/j.jco.2011.03.002" @default.
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