Tauberian theorems for weighted means of double sequences

We discuss the relations between weighted mean methods and ordinary convergence for double sequences. In particular, we study Tauberian theorems also for methods not being products of the related one-dimensional summability methods. For the special case of theC _1,1-method, the results contain a classical Tauberian theorem by Knopp 9] as special case and generalize theorems given by Móricz 16] thereby showing that one of his Tauberian conditions can be weakened.