Composition operators on Hardy spaces of the homogenous rooted trees

In Muthukumar and Ponnusamy (Bull Malays Math Sci Soc 40(4):1801–1815, 2017), the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space Tp defined on a homogeneous rooted tree. In this article, we give equivalent conditions for the composition operator Cϕ to be bounded on Tp and on Tp, spaces and compute their operator norm. We also characterize invertible composition operators as well as isometric composition operators on Tp and on Tp, spaces. Also, we discuss the compactness of Cϕ on Tp and finally prove there are no compact composition operators on Tp, spaces.