高维空间中的Bargmann变换的有界性

Boundedness of Bargmann transformations on high-dimensional spaces

众所周知,一维空间中的Bargmann变换B:L2(R)→F2(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Lp(Rn)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.

It is well known that a Bargmann transform B:L2(R)→F2(C)on R1 is a unitary operator.This paper mainly studies Bargmann transforms on Rn,and the boundedness of the Bargmann transform from Lp(Rn)to Fock spaces when p≠2.Based on the relationship between classical integral transformation and Bargmann transformation,an alternative method is introduced to discuss the boundedness of Bargmann transformation on Rn.