Clifford单基因Bergman空间上的Bergman算子

IF 1.2 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-07-18 DOI:10.1007/s00006-025-01401-x

Karen Avetisyan, Klaus Gürlebeck

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引用次数: 0

摘要

Ren和Malonek已经研究了真实球\({\mathbb R}^n\)上Clifford单基因Bergman空间上的加权Bergman投影算子。我们通过考虑更一般的Bergman非投影算子，并给出它们在加权Lebesgue空间上有界的充分必要条件，扩展和推广了它们的结果。给出了加权单基因Bergman核的锐利估计。

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Bergman Operators on Clifford Monogenic Bergman Spaces

Weighted Bergman projection operators on the Clifford monogenic Bergman spaces over the real ball of \({\mathbb R}^n\) have been already studied in a paper of Ren and Malonek. We extend and generalize their results by considering more general Bergman nonprojection operators and stating a necessary and sufficient condition for them to be bounded on weighted Lebesgue spaces. Sharp estimates for the weighted monogenic Bergman kernel are also given.

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.