Bergman型算子的$L^p$-$L^q$有界性和紧性

Pub Date : 2022-01-01 DOI:10.11650/tjm/220101

Lijia Ding, Kai Wang

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引用次数: 6

摘要

.我们研究了复单位球上的Bergman型算子，它们是由改进的Bergman-kernel诱导的奇异积分算子。我们考虑Bergman型算子的Lp-Lq有界性和紧致性。有界性的结果可视为单位球情形下的Hardy–Littlewood–Sobolev（HLS）型定理。我们还给出了Bergman型算子的一些尖锐范数估计，它实际上给出了单位球上HLS型不等式中最优常数的上界。此外，还给出了一个迹公式。

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The $L^p$-$L^q$ Boundedness and Compactness of Bergman Type Operators

. We investigate Bergman type operators on the complex unit ball, which are singular integral operators induced by the modiﬁed Bergman kernel. We consider the L p - L q boundedness and compactness of Bergman type operators. The results of boundedness can be viewed as the Hardy–Littlewood–Sobolev (HLS) type theorem in the case unit ball. We also give some sharp norm estimates of Bergman type operators which in fact gives the upper bounds of the optimal constants in the HLS type inequality on the unit ball. Moreover, a trace formula is given.

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