Generalization of Schur’s Test and its Application to a Class of Integral Operators on the Unit Ball of \({\mathbb C^n}\)
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- 作者：Ruhan Zhao
- 关键词：Primary 47G10 ; Secondary 32A36 ; Generalized Schur’s test ; integral operators ; weighted L p spaces ; weighted Bergman spaces
- 刊名：Integral Equations and Operator Theory
- 出版年：2015
- 出版时间：July 2015
- 年：2015
- 卷：82
- 期：4
- 页码：519-532
- 全文大小：500 KB
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8.Zhu K.: Operator theory in function spaces. 2nd edn. American Mathematical Society, Rhode Island (2007)View Article MATH - 作者单位：Ruhan Zhao (1)
1. Department of Mathematics, SUNY Brockport, Brockport, NY, 14420, USA - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Analysis - 出版者：Birkh盲user Basel
- ISSN：1420-8989
文摘
We generalize the classical Schur’s test to the boundedness of integral operators from L p to L q spaces equipped with possibly different measures, for \({1\le p\le q < \infty}\) . As an application, we determine exactly when a class of integral operators are bounded from \({L^p(\mathbb{B}_{n},dv_{\alpha})}\) to \({L^q(\mathbb{B}_{n},dv_{\beta})}\) , where \({1\le p\le q < \infty, \mathbb{B}_{n}}\) is the unit ball of n-dimensional complex Euclidean space \({\mathbb{C}^n}\) , and \({dv_{\alpha}}\) and \({dv_{\beta}}\) are weighted area measures on \({\mathbb{C}^n}\) . The result generalizes a result by Kures and Zhu.