发表机构
University of Novi Sad; Ss. Cyril and Methodius University in Skopje（诺维萨德大学; 圣西里尔和梅托迪乌斯科普耶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究相对于一般Banach空间的分布空间上的拉回，证明微分同胚诱导拓扑同构，并探讨常秩光滑映射情形。
AI 中文摘要
我们考虑开集U上的分布空间$\mathcal{D}'^E_L(U)$，其中相对于Banach空间E测得的波前集位于$U\times(\mathbb{R}^n\backslash\{0\})$的闭锥子集L中。Banach空间E仅满足温和的技术假设。我们证明，微分同胚$f:O\rightarrow U$的拉回是拓扑同构$f^*:\mathcal{D}'^E_L(U)\rightarrow\mathcal{D}'^E_{f^*L}(O)$。当E为阶$r\in\mathbb{R}$的$L^p$-Sobolev空间$W^{r,p}(\mathbb{R}^n)$时，我们研究常秩光滑映射$f:O\rightarrow U$的拉回。
英文摘要
We consider the space $\mathcal{D}'^E_L(U)$ of all distributions on the open set $U$ whose wave front set measured with respect to a Banach space $E$ lies in a closed conic subset $L$ of $U\times(\mathbb{R}^n\backslash\{0\})$. The Banach space $E$ only satisfies mild technical assumptions. We show that the pullback by a diffeomorphism $f:O\rightarrow U$ is a topological isomorphism $f^*:\mathcal{D}'^E_L(U)\rightarrow\mathcal{D}'^E_{f^*L}(O)$. In the case when $E$ is the $L^p$-Sobolev space $W^{r,p}(\mathbb{R}^n)$ of order $r\in\mathbb{R}$, we study the pullback by a smooth map $f:O\rightarrow U$ of constant rank.
