International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 545-554
doi:10.1155/IJMMS.2005.545
Bilinear multipliers and transference
Departamento de Análisis Matemático, Universitat de València, Burjassot 46100, València, Spain
Received 26 April 2004; Revised 29 October 2004
Copyright © 2005 Oscar Blasco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We give de Leeuw-type transference theorems for bilinear multipliers. In particular, it is shown that bilinear multipliers arising from regulated functions
m(ξ,η) in ℝ×ℝ can be transferred to bilinear multipliers acting on 𝕋×𝕋 and ℤ×ℤ. The results follow from the description of bilinear multipliers on the discrete real line acting on Lp-spaces.