I am going to speak about joint results with A.B. Aleksandrov.

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.

We obtain such Lipschitz type estimates for functions $f$ in the Besov space $B_{\be,1}^1$ that are analytic in the upper half-plane. For this purpose 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.