Let U be an open subset of \(\mathbb {C}\) with boundary point \(x_0\) and let \(A_{\alpha }(U)\) be the space of functions analytic on U that belong to lip\(\alpha (U)\), the “little Lipschitz class”. We consider the condition \(S= \sum _{n=1}^{\infty }2^{(t+\lambda +1)n}M_*^{1+\alpha }(A_n \setminus U)< \infty ,\) where t is a non-negative integer, \(0<\lambda <1\), \(M_*^{1+\alpha }\) is the lower \(1+\alpha \) dimensional Hausdorff content, and \(A_n = \{z: 2^{-n-1}<|z-x_0|<2^{-n}\). This is similar to a necessary and sufficient condition for bounded point derivations on \(A_{\alpha }(U)\) at \(x_0\). We show that \(S= \infty \) implies that \(x_0\) is a \((t+\lambda )\)-spike for \(A_{\alpha }(U)\) and that if \(S<\infty \) and U satisfies a cone condition, then the t-th derivatives of functions in \(A_{\alpha }(U)\) satisfy a Hölder condition at \(x_0\) for a non-tangential approach.

令U为边界为\（x_0 \）的\（\ mathbb {C} \）的开放子集，令\（A _ {\ alpha}（U）\）为分析U上属于嘴唇的函数的空间\（\ alpha（U）\），“小Lipschitz类”。我们考虑条件\（S = \ sum _ {n = 1} ^ {\ infty} 2 ^ {（t + \ lambda +1）n} M _ * ^ {1+ \ alpha}（A_n \ setminus U）<\ infty，\）其中t是一个非负整数，\（0 <\ lambda <1 \），\（M _ * ^ {1+ \ alpha} \）是较低的\（1+ \ alpha \）维Hausdorff内容和\（A_n = \ {z：2 ^ {-n-1} <| z-x_0 | <2 ^ {-n} \）。这类似于\（x_0 \）处\（A _ {\ alpha}（U）\）上有界点推导的充要条件。我们证明\（S = \ infty \）意味着\（x_0 \）是\（A _ {\ alpha}（U）\）的\（（t + \ lambda）\）尖峰，如果\（S <\ infty \）且U满足圆锥条件，则\（A _ {\ alpha}（U）\）中函数的t阶导数在非切线方法中满足\（x_0 \）的Hölder条件。