  The main objective of the paper is to obtain sharp Lipschitz type estimates
for the norm of operator differences $f(L_1,M_1)-f(L_2,M_2)$ for pairs
$(L_1,M_1)$ and $(L_2,M_2)$ of commuting maximal dissipative operators. To
obtain such estimates, we use double operator integrals with respect to
semi-spectral measures associated with the pairs $(L_1,M_1)$ and $(L_2,M_2)$.
Note that the situation is considerably more complicated than in the case of
functions of two commuting contractions and to overcome difficulties we had to
elaborate new techniques. We deduce from the main result H\"older type
estimates for operator differences as well as their estimates in Schatten--von
Neumann norms.
