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We study perturbations of functions $f(A,B)$ of noncommuting self-adjointoperators $A$ and $B$ that can be defined in terms of double operatorintegrals. 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 Schatten--von Neumannnorm $\bS_p$, $1\le p\le2$ norm:$\|f(A_1,B_1)-f(A_2,B_2)\|_{\bS_p}\le\const(\|A_1-A_2\|_{\bS_p}+\|B_1-B_2\|_{\bS_p})$.However, the condition $f\in B_{\be,1}^1(\R^2)$ does not imply the Lipschitztype estimate in $\bS_p$ with $p>2$. The main tool is Schatten--von Neumannnorm estimates for triple operator integrals.

Triple operator integrals in Schatten--von Neumann norms and functions of perturbed noncommuting operators