In this paper we solve a problem posed by Bommier-Hato et al. (J Math Anal Appl 389:1086–1104, 2012) on the boundedness of the Bergman-type projections in generalized Fock spaces. It will be a consequence of two facts: a full description of the embeddings between generalized Fock–Sobolev spaces and a complete characterization of the boundedness of the above Bergman type projections between weighted \(L^p\)-spaces related to generalized Fock–Sobolev spaces.

中文翻译：

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Bergman投影在$$ {{{\ mathbb {C}}} ^ n $$ Cn上的广义Fock-Sobolev空间上的有界性

在本文中，我们解决了Bommier-Hato等人提出的问题。（J Math Anal Appl 389：1086–1104，2012）关于广义Fock空间中Bergman型投影的有界性。这将是两个事实的结果：对广义Fock-Sobolev空间之间的嵌入的完整描述以及对与广义Fock-相关的加权\（L ^ p \）-空间之间上述Bergman型投影的有界性的完整表征。Sobolev空间。