New results on restriction of multipliers

Salvador Rodrıguez

Universitat de Barcelona

The theorem of K. de Leeuw on restriction of Fourier multipliers says that if ${\bf {m}}$ is a multiplier for $L^p(\mathbb{R})$, then $({\bf {m}}(n))_{n\in \mathbb{Z}}$ is a Fourier multiplier for $L^p(\mathbb{T})$.

In this talk, we extend this result to general rearrangement invariant function spaces. The techniques used are the so called Transference methods due to R.R. Coifman and G. Weiss.