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

Published:2012-10-03
Printed: Jun 2013
• Oscar Blasco de la Cruz,
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain
• Paco Villarroya Alvarez,
Centre for Mathematical Sciences, University of Lund, Lund, 22100, Sweden
 Format: LaTeX MathJax PDF

## Abstract

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
 MSC Classifications: 42B15 - Multipliers 42B35 - Function spaces arising in harmonic analysis

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