The Möbius Invariant QTH Spaces

Abstract

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