An integral operator induced by a Zygmund function

作者：Hu Yun; Song Jinrong; Wei Huaying; Shen Yuliang^*

来源：Journal of Mathematical Analysis and Applications, 2013, 401(2): 560-567.

DOI：10.1016/j.jmaa.2012.12.049

• Zygmund function
• Quasiconformal deformation
• Integral operator

We introduce a kernel function induced by a continuous function f on the unit circle, and show that the corresponding integral operator on the standard Bergman space is a bounded, compact or Hilbert-Schmidt operator precisely when f belongs to the big Zygmund class Lambda(*), the little Zygmund class lambda(*) or the Sobolev class H-3/2, respectively. This may be considered as the infinitesimal version of the main result obtained in Hu and Shen (2012) [9] by two of the authors.

• 出版日期2013-5
• 单位苏州大学