高维空间中的 Bargmann 变换的有界性

众所周知,一维空间中的Bargmann变换B:L~2(R)→F~2(C)是一个酉算子.本文对高维空间中Bargmann变换给出了当p≠2时从L~p(R~n)到Fock空间上Bargmann变换的有界性刻画.此外,基于经典积分变换与Bargmann变换之间的关系,本文引入了另一种方法来讨论高维空间中的Bargmann变换的有界性.

Boundedness of Bargmann transformations on high-dimensional spaces

It is well known that the Bargmann transform $B:L^2(\R)\to F^2(\C)$ is a unitary operator. This paper mainly studies the Bargmann transform in the $n$-dimensional case, and gives the boundedness of the Bargmann transform from \ $L^p(\R^n)$ to Fock spaces when $p\neq2$. Based on the relationship between classical integral transformation and Bargmann transformation, another method is introduced to discuss the boundedness of Bargmann transformation in high dimensional case.\\