The purpose of this paper is to describe a unified approach to proving vector-valued inequalities without relying on the full strength of weighted theory. Our applications include the Fefferman-Stein and Córdoba-Fefferman inequalities, as well as the vector-valued Carleson operator. Using this approach we also produce a proof of the boundedness of the classical bi-parameter multiplier operators, which does not rely on product theory. Our arguments are inspired by the vector-valued restricted type interpolation used by Bateman and Thiele (2013).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-11,
author = {Ciprian Demeter and Prabath Silva},
title = {Some new light on a few classical results},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {129-147},
zbl = {1325.42010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-11}
}
Ciprian Demeter; Prabath Silva. Some new light on a few classical results. Colloquium Mathematicae, Tome 139 (2015) pp. 129-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-11/