非交换自伴算子函数的交换子估计
Commutator estimates for functions of noncommuting self-adjoint operators
AI总结：
该论文研究了Schatten-von Neumann类S_p中自伴算子对的函数演算的交换子估计，得出p≤2时演算满足交换子Lipschitz估计且模S_p可乘，p>2及算子范数下无此估计的结论。
AI中文摘要：
我们研究当自伴算子A与B的交换子[A,B]属于Schatten-von Neumann类S_p时，演算φ↦φ(A,B)的性质。结果表明，当p≤2时，定义在Besov类B_{∞,1}^1(R²)上的该演算满足交换子Lipschitz估计，且在模S_p下是可乘的；而当p>2时，不存在交换子Lipschitz估计，在算子范数下也不存在该估计。
英文摘要：
We study properties of the calculus $φ\mapstoφ(A,B)$ for self-adjoint operators with commutator $[A,B]$ in the Schaten--von Neumann class $\boldsymbol{S}_p$. It turns out that this calculus defined on the Besov class $B_{\infty,1}^1({\Bbb R}^2)$ in the case $p\le2$ admits a commutator Lipschitz estimate and is multiplicative modulo $\boldsymbol{S}_p$. On the other hand in the case $p>2$ there is no commutator Lipschitz estimate. There is no commutator Lipschitz estimate in the operator norm as well.
