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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
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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 Fourier multipliers, restriction theorems, weighted spaces
MSC Classifications: 42B15, 42B35 show english descriptions Multipliers
Function spaces arising in harmonic analysis
42B15 - Multipliers
42B35 - Function spaces arising in harmonic analysis
 

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