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 Estimates for the Higher Order Riesz Transforms related to Schr\"odinger type operators Bull. Korean Math. Soc.Published online November 3, 2020 Yanhui Wang Jiaozuo University Abstract : We consider the Schr\"odinger type operator $\mathcal{L}_k=(-\Delta)^k+V^k$ on $\mathbb{R}^n ( n\geq 2k+1)$, where $k=1,2$ and the nonnegative potential $V$ belongs to the reverse H\"older class $RH_s$ with \( n/21/2,$where$p_1=\frac{n}{4(\beta-\alpha)}, p_2=\frac{n}{n-4(\beta-\alpha)}.$Moreover, we prove that$T_{\alpha,\beta}$is bounded from$BMO_{\mathcal{L}_1}(\mathbb{R}^n)$to itself when$\beta-\alpha=1/2.\$ Keywords : Riesz transform, Schr\"odinger operator, Hardy space, BMO. MSC numbers : 42B30; 35J10; 42B35 Full-Text :