Semiclassical Lp estimates of quasimodes on submanifolds

Melissa Tacy*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    34 Citations (Scopus)


    Let P = P(h) be a semiclassical pseudodifferential operator on a Riemannian manifold M. Suppose that u(h) is a localized, L2 normalized family of functions such that P(h)u(h) is O(h) in L2, as h → 0. Then, for any submanifold Y ⊂ M, we obtain estimates on the Lp norm of u(h) restricted to Y, with exponents that are sharp for h → 0. These results generalize those of Burq et al. [4] on Lp norms for restriction of Laplacian eigenfunctions. As part of the technical development we prove some extensions of the abstract Strichartz estimates of Keel and Tao [8].

    Original languageEnglish
    Pages (from-to)1538-1562
    Number of pages25
    JournalCommunications in Partial Differential Equations
    Issue number8
    Publication statusPublished - Aug 2010


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