Integration operators on Hardy-Carleson type tent spaces

Abstract

We completely characterize the boundedness and compactness of Volterra type integration operators Jb between Hardy-Carleson type tent spaces CTp,α. Furthermore, we show that the compactness and strict singularity of Jb:CTp,α→CTp,α are equivalent for all 1≤p<∞ and α>−n−1. Our tools mainly involve the atomic decomposition for the space CTp,α, Khinchine's inequality and multipliers of some sequence tent spaces. Corresponding results are also obtained for the little spaces CTp,α0.