On zero varieties of holomorphic functions in Hardy spaces |
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Authors: | So-Chin Chen |
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Institution: | Department of Mathematics, National Tsing Hua University, Hsinchu 30043, Taiwan, ROC |
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Abstract: | In contrast to the famous Henkin-Skoda theorem concerning the zero varieties of holomorphic functions in the Nevanlinna class on the open unit ball Bn in , n?2, it is proved in this article that for any nonnegative, increasing, convex function ?(t) defined on , there exists satisfying such that there is no f∈Hp(Bn), 0<p<∞, with . Here Ng(ζ,1) denotes the integrated zero counting function associated with the slice function gζ. This means that the zero sets of holomorphic functions belonging to the Hardy spaces Hp(Bn), 0<p<∞, unlike that of the holomorphic functions in the Nevanlinna class, cannot be characterized in the above manner. |
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Keywords: | Hardy spaces Nevanlinna class Blaschke condition |
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