Some new light on a few classical results
Volume 140 / 2015
Colloquium Mathematicum 140 (2015), 129-147
MSC: Primary 42B20; Secondary 42B25.
DOI: 10.4064/cm140-1-11
Abstract
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).
