On a general class of operators

We consider a new class of operators on abstract measure spaces, involving a series of operators in Harmonic Analysis (Calderόn-Zygmund operators, fractional maximal function, Riesz potentials, martingale transforms, Beurling-Ahlfors transform, Carleson type operators, some types of Littlewood-Paley square functions, etc.). We will introduce several basic properties of those general operators, which improve some results obtained by different authors in recent years.