Let
f
f
be a function on
R
2
\mathbb {R}^2
in the inhomogeneous Besov space
{\text \textit {\Russian {B}}}_{\infty ,1}^{1}(\mathbb {R}^2). For a pair
(
A
,
B
)
(A,B)
of not necessarily bounded and not necessarily commuting self-adjoint operators, the function
f
(
A
,
B
)
f(A,B)
of
A
A
and
B
B
is introduced as a densely defined linear operator. It is shown that if
1
≤
p
≤
2
1\le p\le 2
,
(
A
1
,
B
1
)
(A_1,B_1)
and
(
A
2
,
B
2
)
(A_2,B_2)
are pairs of not necessarily bounded and not necessarily commuting selfadjoint operators such that both
A
1
−
A
2
A_1-A_2
and
B
1
−
B
2
B_1-B_2
belong to the Schatten–von Neumann class
S
p
{\boldsymbol {S}}_p
and
f\in {\text \textit {\Russian {B}}} _{\infty ,1}^{1}(\mathbb {R}^2), then the following Lipschitz type estimate holds:
\begin{equation*} \|f(A_1,B_1)-f(A_2,B_2)\|_{{\boldsymbol {S}}_p} \le \operatorname {const}\|f\|_{\text \textit {\Russian {B}}_{\infty ,1}^{1}}\max \big \{\|A_1-A_2\|_{{\boldsymbol {S}}_p},\|B_1-B_2\|_{{\boldsymbol {S}}_p}\big \}. \end{equation*}