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In this article we prove that for $p>2$, there exist pairs of self-adjointoperators $(A_1,B_1)$ and $(A_2,B_2)$ and a function $f$ on the real line inthe homogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$ such that thedifferences $A_2-A_1$ and $B_2-B_1$ belong to the Schatten--von Neumann class$\boldsymbol{S}_p$ but $f(A_2,B_2)-f(A_1,B_1)\not\in\boldsymbol{S}_p$. Asimilar result holds for functions of contractions. We also obtain an analog ofthis result in the case of triples of self-adjoint operators for any $p\ge1$

Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$