论文标题
Hermite型操作员分数幂的侧面收敛
Pointwise convergence of fractional powers of Hermite type operators
论文作者
论文摘要
当$ l $是Hermite或Ornstein-Uhlenbeck操作员时，我们会在功能$ f $上找到最小的集成性和平滑性条件，以便在给定点$ x_0 $的情况下，分数功率$ l^σf（x_0）$在给定的点上定义很好。我们用各种示例说明了条件的最佳性。最后，我们获得了分数运算符的类似结果$（-Δ+r）^σ$，$ r> 0 $。
When $L$ is the Hermite or the Ornstein-Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function $f$ so that the fractional power $L^σf(x_0)$ is well-defined at a given point $x_0$. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators $(-Δ+R)^σ$, with $R>0$.
