The Mobius Invariant QHT Spaces

In this article, we introduce a new space of harmonic mappings that is an extension of the well known space Q(T) in the unit disk D in term of non decreasing function. Several characterizations of the space Q(H)(T) are investigated. We also define the little subspace of Q(H)(T). Finally, the boundedness of the composition operators C-f mapping into the space Q(H)(T) and Q(H,0)(T) are considered.