TITLE:
β-Hausdorff Operator on Lipschitz Space in the Unit Polydisk
AUTHORS:
Chaofeng Zhang, Rong Hu
KEYWORDS:
Unit Polydisk, Lipschitz Space, β-Hausdorff Operator, Weighted Composition Operator
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.5,
May
5,
2014
ABSTRACT:
In this paper, we define β-Hausdorff operator on the unit polydisk
and study the boundedness of the operator on Lipschitz space. Firstly, we
translate the problem of coefficient into integral of weighted composition operator, then give the sufficient conditions of boundedness, and also obtain
an upper bound for the operator norm on Lipschitz space.