Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/12096
Title: | The Marcinkiewicz Interpolation Theorem and its Extensions |
Authors: | Vaughan, Charles David |
Advisor: | Heinig, H. P. |
Department: | Mathematics |
Keywords: | Mathematics;Mathematics |
Publication Date: | Nov-1978 |
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> |
URI: | http://hdl.handle.net/11375/12096 |
Identifier: | opendissertations/701 1898 1074006 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
---|---|---|---|
fulltext.pdf | 2.55 MB | Adobe PDF | View/Open |
Items in MacSphere are protected by copyright, with all rights reserved, unless otherwise indicated.