Boundary multipliers of a family of Möbius invariant spaces

Abstract

For $1<p<\infty$ and $0<s<1$, we consider the function spaces $\mathcal{Q}_s^p(\mathbb{T})$ that appear naturally as the space of boundary values of a certain family of analytic Möbius invariant function spaces on the the unit disk. In this paper, we give a complete description of the pointwise multipliers going from $Q_s^{p_1}(\mathbb{T})$ to $Q_r^{p_2}(\mathbb{T})$ for all ranges of $1<p_1, p_2<\infty$ and $0<s,r<1$. The spectra of such multiplication operators is also obtained.