L^p-multipliers for the Hilbert space valued functions on the Heisenberg group

It is well known that if m is an Lp-multiplier for the Fourier transform on ℝn, (1 < p < ∞) then there exists a pseudomeasure σ such that Tm f = σ * f. A similar problem is discussed for the Lp-Fourier multipliers for H-valued functions on the Heisenberg group, where H is a separable Hilbert space. © Springer-Verlag 2009.