加权复合算子在两类函数空间之间的序有界性

Order Boundedness of Weighted Composition Operators Between Two Classes of Function Spaces

本文首先研究了加权复合算子W_(Φ,φ)(f):=Φfoφ的Hilbert-Schmidt性质与序有界性的对应关系.接着利用加权Dirichlet空间D^(q)_(β)(0<q<∞,-1<β<∞)以及导数Hardy空间S^(p)(0<p<∞)上的点值泛函δ_(z)以及导数点值泛函δ’_(z)的范数估计,给出了加权复合算子W_(Φ,φ)在加权Dirichlet空间D^(q)_(β)与导数Hardy空间S^(p)之间的序有界性的完整刻画.

In this paper,we first investigate the correspondence between order boundedness and Hilbert-Schmidt of weighted composition operators W_(Φ,φ)(f):=-Φfoφ.Then,by resorting to the estimates of the norms of point evaluation functionalsδ_(z) and derivative point evaluation functionalsδ’_(z) on weighted Dirichlet spaces D^(q)_(β)(0<q<∞,-1<β<∞)and derivative Hardy spaces S^(p)(0<p<∞),the order boundedness of weighted composition operators W_(Φ,φ)between weighted Dirichlet spaces D^(q)_(β) and derivative Hardy spaces S^(p) are completely characterized.