1. CJM 2012 (vol 65 pp. 510)
|Transference of vector-valued multipliers on weighted $L^p$-spaces|
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.
Keywords:Fourier multipliers, restriction theorems, weighted spaces