Abstract
In this paper, we attempt to investigate a new harmonic mapping class denoted by the Banach space Q(H)(p) in the unit disk. Several characteristics of the class Q(p) are examined. We additionally describe some findings for the little Q(H)(p) harmonic space, which really is a closed subspace of Q(H)(p). We also talk about the boundedness and compactness of the composition operator in the Q(H)(p)space.