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DC Field | Value | Language |
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dc.contributor.advisor | Heinig, H. P. | en_US |
dc.contributor.author | Vaughan, Charles David | en_US |
dc.date.accessioned | 2014-06-18T16:58:15Z | - |
dc.date.available | 2014-06-18T16:58:15Z | - |
dc.date.created | 2009-11-29 | en_US |
dc.date.issued | 1978-11 | en_US |
dc.identifier.other | opendissertations/701 | en_US |
dc.identifier.other | 1898 | en_US |
dc.identifier.other | 1074006 | en_US |
dc.identifier.uri | http://hdl.handle.net/11375/12096 | - |
dc.description.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> | en_US |
dc.subject | Mathematics | en_US |
dc.subject | Mathematics | en_US |
dc.title | The Marcinkiewicz Interpolation Theorem and its Extensions | en_US |
dc.type | thesis | en_US |
dc.contributor.department | Mathematics | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 2.55 MB | Adobe PDF | View/Open |
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