%A 邓冠铁, 付倩, 曹辉 %T LAPLACE TRANSFORMS FOR ANALYTIC FUNCTIONS IN TUBULAR DOMAINS %0 Journal Article %D 2021 %J 数学物理学报(英文版) %R 10.1007/s10473-021-0610-6 %P 1938-1948 %V 41 %N 6 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16577.shtml} %8 2021-12-25 %X Assume that $ 0< p<\infty $ and that $B$ is a connected nonempty open set in $\mathbb{R}^n$, and that $A^{p}(B)$ is the vector space of all holomorphic functions $F$ in the tubular domains $\mathbb{R}^n+{\rm i}B$ such that for any compact set $ K \subset B,$ $$ \|y\mapsto \|x\mapsto F(x+{\rm i}y)\|_{L^p(\mathbb{R}^n)}\|_{L(K)}<\infty, $$ so $A^p(B)$ is a Fréchet space with the Heine-Borel property, its topology is induced by a complete invariant metric, is not locally bounded, and hence is not normal. Furthermore, if $1\leq p\leq 2$, then the element $F$ of $A^{p}(B)$ can be written as a Laplace transform of some function $f\in L(\mathbb{R}^n)$.