Hölder conditions and $$\tau $$-spikes for analytic Lipschitz functions

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