从Hardy空间到对数Hardy-Bloch型空间BH_(p,L)的加权复合算子

Weighted Composition Operators from Hardy to Logarithmic Hardy-Bloch Spaces

讨论了从单位圆盘上的Hardy空间Hp到对数Hardy-Bloch型空间BH p,L={f∈H(D):‖f‖p,L=sup z∈D(1-|z|)M p(|z|,f')log(e/1-|z|)<∞}的加权复合算子uCφ的有界性与紧性,主要得到以下结论:(i)uCφ是空间H∞到BH p,L(1≤p<∞)的有界算子与紧算子的充要条件;(ii)uCφ是空间Hq(1≤q<∞)到BH p,L(1≤p<∞)的有界算子与紧算子的充要条件.

The boundedness and compactness of the weighted composition operator uCφ fromHardy spaces Hp to Hardy-Bloch-type spaces BH_P,L={f∈H（D）：‖f‖P,L=sup z∈D （1-｜z｜）M_P （｜z｜,f′）log（e/1-｜z｜）〈∞} Mp are researched. It is obtained as follows. （i） Some necessaryand sufficient conditions are given for which uC is a bounded operator or compact from H∞ toBH_P,L （1≤p〈∞） ; （ii） some necessary and sufficient conditions are given for which uCφ is a bounded operator or compact from Hq （1≤p〈∞） to BH_P,L （1≤p〈∞）.