论文标题
在Seeley型上半部空间的通用延长运算符上
On Seeley-type Universal Extension Operators for the Upper Half Space
论文作者
论文摘要
通过反射原则从标准半空间扩展中修改，我们为上半部空间构建了一个线性扩展操作员$ \ bbb r^n _+$，其具有$ ef（x）= \ sum_ {j = - \ \ \ \ \ \ iffty}^\ infty}^\ infty a_jf（x'， - b_jx_n）$ for $ x_n <0。我们证明，$ e $在所有$ c^k $ spaces，Sobolev和HölderSpaces，Besov和Triebel-Lizorkin的空间中都限制在其Morrey概括中。我们还对有限的平滑域进行了类似的结构。
Modified from the standard half-space extension via reflection principle, we construct a linear extension operator for the upper half space $\Bbb R^n_+$ that has the form $Ef(x)=\sum_{j=-\infty}^\infty a_jf(x',-b_jx_n)$ for $x_n<0$. We prove that $E$ is bounded in all $C^k$-spaces, Sobolev and Hölder spaces, Besov and Triebel-Lizorkin spaces, along with their Morrey generalizations. We also give an analogous construction on bounded smooth domains.
