The Bargmann transform on L-p(R)
The Bargmann transform on L-p(R)
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Lp(R) 上的 Bargmann 变换
DOI：
10.1016/j.jmaa.2018.08.031
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发表时间：
2018
影响因子：
1.3
通讯作者：
Hou Shengzhao
中科院分区：
文献类型：
--
作者：
Cao Guangfu;He Li;Hou Shengzhao
研究了Bargmann变换B在实直线的L p空间上的映射性质。众所周知，B等距映射L 2(R)到Fock空间F2上.当2<；p≤∞时，我们证明了B将L p(R)有界映射到Fock空间Fp上，且该映射不在上.当1≤p<；2时，我们证明了B将L p(R)有界地映射到Fq中，其中1/p+1/q=1，并且B不将L p(R)映射到Fp中.当0<；p<；1时，没有合理的方法定义L p(R)上的Bargmann变换.
We study the mapping properties of the Bargmann transform B on L p spaces of the real line. It is well known that B maps L 2 (R) isometrically onto the Fock space F 2. When 2< p≤∞, we show that B maps L p (R) boundedly into the Fock space F p and that the mapping is not onto. When 1≤ p< 2, we show that B maps L p (R) boundedly into the Fock space F q, where 1/p+ 1/q= 1, and that B does not map L p (R) into F p. There is no reasonable way to define the Bargmann transform on L p (R) when 0< p< 1.