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    Linear and multilinear fractional operators: weighted inequalities, sharp bounds, and other properties

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    Moen_ku_0099D_10309_DATA_1.pdf (635.4Kb)
    Issue Date
    2009-04-27
    Author
    Moen, Kabe
    Publisher
    University of Kansas
    Format
    143 pages
    Type
    Dissertation
    Degree Level
    Ph.D.
    Discipline
    Mathematics
    Rights
    This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
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    Abstract
    In this work we consider various fractional operators, including the classical fractional integral operators, related fractional maximal functions, multilinear fractional integral operators, and multisublinear fractional maximal functions. We characterize the weighted inequalities for the multilinear fractional operators, and examine more general two-weight inequalities giving sufficient conditions for their boundedness. For the classical fractional integral operator we obtain sharp bounds on the operator norm between weighted Lebesgue spaces in terms of the constant associated to the weight. We also introduce a more general fractional maximal operators, characterize their boundedness on weighted Lebsegue spaces, and obtain sharp bounds on the operator norms in terms of the weighted constants. Finally, we examine singular integral operators and fractional integral operators acting on mixed Lebesgue spaces with weights. We provide endpoint estimates for singular integrals and an off-diagonal extrapolation theorem.
    URI
    http://hdl.handle.net/1808/5445
    Collections
    • Dissertations [3958]
    • Mathematics Dissertations and Theses [113]

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    785-864-8983
    KU Libraries
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    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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