Let a function
f
f
belong to the inhomogeneous analytic Besov space
(
B
∞
,
1
1
)
+
(
R
2
)
(B_{\infty ,1}^{\,1})_+(\mathbb {R}^2)
. For a pair
(
L
,
M
)
(L,M)
of not necessarily commuting maximal dissipative operators, the function
f
(
L
,
M
)
f(L,M)
of
L
L
and
M
M
is defined as a densely defined linear operator. For
p
∈
[
1
,
2
]
p\in [1,2]
, it is proved that if
(
L
1
,
M
1
)
(L_1,M_1)
and
(
L
2
,
M
2
)
(L_2,M_2)
are pairs of not necessarily commuting maximal dissipative operators such that both differences
L
1
−
L
2
L_1-L_2
and
M
1
−
M
2
M_1-M_2
belong to the Schatten–von Neumann class
S
p
{\boldsymbol S}_p
, then for an arbitrary function
f
f
in
(\mathcyr {B}_{\infty ,1}^{\,1})_+(\mathbb {R}^2), the operator difference
f
(
L
1
,
M
1
)
−
f
(
L
2
,
M
2
)
f(L_1,M_1)-f(L_2,M_2)
belongs to
S
p
{\boldsymbol S}_p
and the following Lipschitz type estimate holds:
\begin{equation*} \|f(L_1,M_1)-f(L_2,M_2)\|_{{\boldsymbol S}_p} \le const\|f\|_{\mathcyr {B}_{\infty ,1}^{\,1}}\max \big \{\|L_1-L_2\|_{{\boldsymbol S}_p},\|M_1-M_2\|_{{\boldsymbol S}_p}\big \}. \end{equation*}