摘要: 在本文我们考虑振幅a属于HÖrmander类
![](https://image.hanspub.org/IMAGE/Edit_c4240bb5-08a2-46e1-a5a6-273f05839aeb.png)
时的拟微分算子T
a在Besov空间上的有界性. 对于0 ≤ ρ ≤ 1, p ≥ 1, 令
![](https://image.hanspub.org/IMAGE/Edit_ba952db2-468b-4eda-b07d-f91a5550c991.png)
如果
![](https://image.hanspub.org/IMAGE/Edit_545ed994-abbb-4217-9233-8392abcc00ae.png)
且s > m − m
0, 我们证明拟微分算子Ta是Besov空间
![](https://image.hanspub.org/IMAGE/Edit_cf589b13-7b55-4d08-a706-13bf17fbc49b.png)
到
![](https://image.hanspub.org/IMAGE/Edit_b16b390b-fed0-4295-a8d8-6ca97b98ed3c.png)
的有界算子. 这个结果推广了Stein的一个小结果.
Abstract:
In this note, we consider the boundedness of the pseudo-differential operator Ta whose symbol a belongs to HÖrmander class
![](https://image.hanspub.org/IMAGE/Edit_4908a3e5-53a2-4bb2-9ce5-c266561c6dda.png)
on Besov spaces.Let 0 ≤ ρ ≤ 1, p ≥ 1
![](https://image.hanspub.org/IMAGE/Edit_69576829-4c14-4a95-af4d-6deb22e4692e.png)
If
![](https://image.hanspub.org/IMAGE/Edit_d499b14f-69fe-4a80-adf3-33f69c330e94.png)
and s > m − m
0, then the pseudo-differential operator T
a is bounded from
![](https://image.hanspub.org/IMAGE/Edit_171da049-ce51-455f-a900-24d7ff5ea94e.png)
to
![](https://image.hanspub.org/IMAGE/Edit_2eb88b62-bb6b-4189-9a30-93c6cc5edf04.png)
. And our work is to generalize a result of Stein.