Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LIPSCHITZ TYPE INEQUALITY IN WEIGHTED BLOCH SPACE Bq

  • Published : 2002.03.01
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Abstract

Let B be the open unit ball with center 0 in the complex space $C^n$. For each q>0, B$_{q}$ consists of holomorphic functions f : B longrightarrow C which satisfy sup z $\in$ B $(1-\parallel z \parallel^2)^q\parallel\nabla f(z)\parallel < \infty$ In this paper, we will show that functions in weighted Bloch spaces $B_{q}$ (0 < q < 1) satifies the following Lipschitz type result for Bergman metric $\beta$: ｜f(z)-f($\omega$)｜< $C\beta$(z, $\omega$) for some constant C.

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