Date of Award
Doctor of Philosophy (PhD)
Dr. H. P. Heinig
This thesis is primarily devoted to the study of the Marcinkiewicz interpolation theorem and its applications.
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.
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.
Vaughan, David Charles, "The Marcinkiewicz Interpolation Theorem and its Extensions" (1978). Open Access Dissertations and Theses. Paper 701.