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|Title:||The Marcinkiewicz Interpolation Theorem and its Extensions|
|Authors:||Vaughan, Charles David|
|Advisor:||Heinig, H. P.|
|Abstract:||<p>This thesis is primarily devoted to the study of the Marcinkiewicz interpolation theorem and its applications.</p> <p>The Marcinkiewicz theorem is extended to function spaces that include both the Lebesgue-Orlicz and Lorentz spaces, namely the rearrangement invariant function spaces. Without imposing any additional hypotheses, weighted generalizations are obtained and applied to well known operators in Fourier analysis.</p> <p>The Hardy spaces of analytic functions do not fall into the class of rearrangement invariant function spaces. However, following Igari's generalization of the Marcinkiewicz theorem to Hardy spaces, a variant and weighted extension are proved and applied to obtain a weighted integral estimate involving the Littlewood-Paley g-function.</p>|
|Appears in Collections:||Open Access Dissertations and Theses|
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