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Transference of Vector-valued Multipliers on Weighted Lp-spaces

Published online by Cambridge University Press:  20 November 2018

Oscar Blasco  and
Paco Villarroya
Oscar Blasco
Affiliation:
Centre for Mathematical Sciences, University of Lund, Lund, 22100, Sweden, e-mail: [email protected]
Paco Villarroya
Affiliation:
Centre for Mathematical Sciences, University of Lund, Lund, 22100, Sweden, e-mail: [email protected]
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Abstract

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New transference results for Fourier multiplier operators defined by regulated symbols are presented. 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 that can be below one.

We also develop some ad-hoc methods that apply to weights defined by the product of periodic weights with functions of power type. Our vector-valued approach allows us to extend our results to transference of maximal multipliers and provide transference of Littlewood–Paley inequalities.

Keywords

42B1542B35Fourier multipliersrestriction theoremsweighted spaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 3 , 01 June 2013 , pp. 510 - 543
Copyright
Copyright © Canadian Mathematical Society 2013

References

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