具有非平凡Fourier型Banach空间的一个特征

A characterization of Banach spaces having a nontrivial Fourier type

设X为复Banach空间,则X具有非平凡Fourier型当且仅当存在(等价地,对所有)0<α<1,任取f∈C^(α)([0,2π];X)满足f(0)=f(2π),都有Σ_(n∈Z)||f(n)||^(1/α)<∞成立.

Let X be a Banach space.We show that X has a nontrivial Fourier type if and only if there exists(equivalently,for all)0<<1,such that for all f∈C^(α)([0;2π];X)satisfying f(0)=f(2),we have Σ_(n∈Z)||f(n)||^(1/α)<∞.