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    • 2016 Dissertations (MU)
    • 2016 MU dissertations - Freely available online
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    Maximal Fourier integrals and multilinear multiplier operators

    Nguyen, Hanh Van (Researcher on mathematics)
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    Date
    2016
    Format
    Thesis
    Metadata
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    Abstract
    The first topic of this dissertation is concerned with the L^2 boundedness of a maximal Fourier integral operator which arises by transferring the spherical maximal operator on the sphere S^n to a Euclidean space of the same dimension. Thus, we obtain a new proof of the boundedness of the spherical maximal function on S^n. In the second part, we obtain boundedness for m-linear multiplier operators from a product of Lebesgue (or Hardy spaces) on R^n to a Lebesgue space on R^n, with indices ranging from zero to infinity. The multipliers lie in an L^2-based Sobolev space on R^{mn} uniformly over all annuli, just as in Hörmander's classical multiplier condition. Moreover, via proofs or counterexamples, we find the optimal range of indices for which the boundedness holds within this class of multilinear Fourier multipliers.
    URI
    https://hdl.handle.net/10355/57249
    https://doi.org/10.32469/10355/57249
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
    Collections
    • 2016 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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