在此篇文章當中, 我們循著當年Brown, Shield 以及 Zeller 的思路, 在高維度的複球上探討關於有界解析函數(bounded holomorphic function)的邊界行為. 在過程中我們也對歐氏空間單位球上實數值有界調和函數以及實數值有界M-調和函數的支配現象作初步的探討

In this article, following the line developed by Brown, Shields and Zeller, we
study the nontangential behavior of holomorphic functions in the unit ball Bn
of Cn: The dominating phenomenon for real bounded harmonic functions in the
unit ball Bn of Rn and M-harmonic functions in the unit ball Bn of Cn are also
investigated.

Contents
1 Introduction 2
2 Preliminary results 3
2.1 An　auxiliary　lemma. . . . . . 3
2.2 Some background from Functional and Complex　Analysis 4
3 The Banach space E(Bn) 6
3.1 Main result . . . . . . . . . . . . . . . . . 6
3.2 Some examples . . . . . . . . . . . . . . . 11
4 Dominating sets for bounded harmonic functions on Bn in Rn 13
5 Dominating sets for bounded M-harmonic functions on Bn of Cn 17
5.1 K-Limit . . . . . . . . . . . . . . . . . . . . . . . 17
5.2 M-harmonic functions . . . . . . . . . . . . . . . 17

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