<i>β</i>-Hausdorff Operator on Lipschitz Space in the Unit Polydisk

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.