We use a bootstrapping property of
R-boundedness to show that some (known)
n-dimensional Fourier multiplier theorems on UMD spaces with property α are immediate corollaries of their one-dimensional versions. The method also gives easy extensions of these results to mixed-norm
L[`(p)]L^{\bar p}
spaces.
Mathematics Subject Classification (2000). 42B15
Received: 15 September 2004