C^n上广义Fock-Sobolev空间上的Hankel双线性形式

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2020-06-01 DOI:10.5186/aasfm.2020.4546

C. Cascante, J. Fàbrega, D. Pascuas

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引用次数: 2

摘要

我们刻画了C上广义Fock-Sobolev空间积上的Hankel双线性形式对权(1 + |z|)e α 2 |z|的有界性，对于l≥1，α > 0， ρ∈r。我们得到了Bergman核的一个弱分解和一个Littlewood - Paley公式，这是证明我们的主要结果的关键成分。作为应用，我们刻画了这些空间上的小Hankel算子的Schatten类的有界性、紧性和隶属性。

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Hankel bilinear forms on generalized Fock–Sobolev spaces on C^n

We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock–Sobolev spaces on C with respect to the weight (1 + |z|)e α 2 |z| , for l ≥ 1, α > 0 and ρ ∈ R. We obtain a weak decomposition of the Bergman kernel with estimates and a Littlewood– Paley formula, which are key ingredients in the proof of our main results. As an application, we characterize the boundedness, compactness and the membership in the Schatten class of small Hankel operators on these spaces.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.