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 Estimates for Riesz Transforms Associated with Schr\"odinger Type Operators Bull. Korean Math. Soc.Published online August 2, 2019 Yueshan Wang Jiaozuo university Abstract : Let $\mathcal{L}_k=(-\Delta)^k+V^k (k=1,2)$ be the Schr\"odinger type operator, where nonnegative potential $V$ belongs to the reverse H\"older class $RH_s, s\geq n/2.$ In this paper, we consider the operator $T_{\alpha,\beta}=V^{2\alpha} \mathcal{L}_2^{-\beta}$ and its adjoint operator $T^*_{\alpha,\beta}$ for $0<\alpha\leq \beta\leq 1.$ We establish the $(L^{p_1},L^{p_2})$-boundedness of operators $T_{\alpha,\beta}$ and $T^*_{\alpha,\beta},$ respectively. We also show that $T_{\alpha,\beta}$ is bounded from Hardy type space $H^1_{\mathcal{L}_1}(\mathbb{R}^n)$ into $L^{p_2}(\mathbb{R}^n)$ and $T^*_{\alpha,\beta}$ is bounded from $L^{p_1}(\mathbb{R}^n)$ into $BMO$ type space $BMO_{\mathcal{L}_1}(\mathbb{R}^n),$ where $p_1=\frac{n}{4(\beta-\alpha)}, p_2=\frac{n}{n-4(\beta-\alpha)}.$ Keywords : Riesz transform; Schr\"odinger operator; Hardy space,; BMO MSC numbers : 42B35; 35J10 Full-Text :