  We consider functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and
$B$ that can be defined in terms of double operator integrals. We prove that if
$f$ belongs to the Besov class $B_{\be,1}^1(\R^2)$, then we have the following
Lipschitz type estimate in the trace norm:
$\|f(A_1,B_1)-f(A_2,B_2)\|_{\bS_1}\le\const(\|A_1-A_2\|_{\bS_1}+\|B_1-B_2\|_{\bS_1})$.
However, the condition $f\in B_{\be,1}^1(\R^2)$ does not imply the Lipschitz
type estimate in the operator norm.
