Superconformal Covariantization Of Superdifferential Operator On (1|1) Superspace And Classical N=2 W-superalgebras

A study of the superconformal covariantization of superdifferential operators defined on $(1|1)$ superspace is presented. It is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order. In such a case, the action of superconformal transformation on the superdifferential operator is nothing but a hamiltonian flow defined by the corresponding supersymmetric second Gelfand-Dickey bracket. The covariant form of a superdifferential operator of odd order is given.