  In this article, we define discrete analogue of generalized Hardy spaces and
its separable subspace on a homogenous rooted tree and study some of its
properties such as completeness, inclusion relations with other spaces,
separability, growth estimate for functions in these spaces and their
consequences. Equivalent conditions for multiplication operators to be bounded
and compact are also obtained. Furthermore, we discuss about point spectrum,
approximate point spectrum and spectrum of multiplication operators and discuss
when a multiplication operator is an isometry.
