Boundary multipliers of a family of Mobius invariant function spaces

For $1<p<infty$ and $0<s<1$, let $mathcal{Q}^p_ s (mathbb{T})$ be the space of those functions $f$ which belong to $ L^p(mathbb{T})$ and satisfy [ sup_{Isubset mathbb{T}}frac{1}{|I|^s}int_Iint_Ifrac{|f(zeta)-f(eta)|^p}{|zeta-eta|^{2-s}}|dzeta||deta|<infty, ] where $|I|$ is the length of an arc $I$ of the unit circle $mathbb{T}$ . In this paper, we give a complete description of multipliers between $mathcal{Q}^p_ s (mathbb{T})$ spaces. The spectra of multiplication operators on $mathcal{Q}^p_ s (mathbb{T})$ are also obtained.