中文摘要：

若p调和函数u属于W^1，q〉p-1〉0，且满足｜p-2｜或｜p—g｜足够小，证明了△↓一定是Holder连续的．这个结果推广了调和函数（p=2）的正则性结论，其证明主要运用了Hodge分解及反Holder不等式．

英文摘要：

Assuming ap harmonic function u in W^1＇q, q 〉p -1 〉 0, withp-2or｜ p-q｜ sufficiently small, this paper proves that Vu must be Holder continuous. This finding extends the result of the regularity of harmonic function （ p = 2 ）. The proofs are derived on the basis of Hodge decomposition and reverse Holder inequalities.