Transference of vector-valued multipliers on weighted $L^p$-spaces

http://dx.doi.org/10.4153/CJM-2012-041-0
Canad. J. Math. 65(2013), 510-543

  Published:2012-10-03
 Printed: Jun 2013

We prove restriction and extension of multipliers between weighted Lebesgue spaces with two different weights, which belong to a class more general than periodic weights, and two different exponents of integrability which can be below one. We also develop some ad-hoc methods which apply to weights defined by the product of periodic weights with functions of power type. Our vector-valued approach allow us to extend results to transference of maximal multipliers and provide transference of Littlewood-Paley inequalities.