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Boundedness of the Bergman Projection on Generalized Fock–Sobolev Spaces on $${{\mathbb {C}}}^n$$Cn
Complex Analysis and Operator Theory ( IF 0.7 ) Pub Date : 2020-03-07 , DOI: 10.1007/s11785-020-00992-6
Carme Cascante , Joan Fàbrega , Daniel Pascuas

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:

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。
更新日期:2020-03-07
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