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

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.