Let \(\mathcal {L}_2=(-\Delta )^2+V^2 \) be the Schrödinger-type operator on \(\mathbb {R}^n (n\ge 5),\) where the nonnegative potential \(V\) belongs to the reverse Hölder class \(RH_s, n/2<s<n.\) The estimates of \(L^p(\mathbb {R}^n)\) and weak type (1, 1) for the Riesz transform \(\nabla \mathcal {L}_2^{-\frac{1}{4}}\) related to Schrödinger-type operators are established.

中文翻译：

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与Schrödinger型算子有关的Riesz变换的一些估计

令\（\ mathcal {L} _2 =（-\ Delta）^ 2 + V ^ 2 \）是\（\ mathbb {R} ^ n（n \ ge 5），\）上的Schrödinger型算子，其中非负电位\（V \）属于反向holder类\（RH_s，N / 2 <S <N。\）的估计\（L ^ p（\ mathbb {R} ^ N）\）和弱类型（ 1，1）建立与Schrödinger型算子相关的Riesz变换\（\ nabla \ mathcal {L} _2 ^ {-\ frac {1} {4}} \）。