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This paper comprises two parts. We first investigate anL  p{L^{p}}   -type of limiting absorption principle for Schrödinger operatorsH  =    -  Δ   +  V{H=-\Delta+V}    onℝ  n{\mathbb{R}^{n}}    (n  ≥  3{n\geq 3}   ), i.e., we prove the ϵ-uniformL    2  ⁢   (   n  +  1   )    /   (   n  +  3   ){L^{{2(n+1)}/({n+3})}}   –L    2  ⁢   (   n  +  1   )    /   (   n  -  1   ){L^{{2(n+1)}/({n-1})}}   -estimates of the resolvent(    H  -  λ   ±   i  ⁢  ϵ    )    -  1{(H-\lambda\pm i\epsilon)^{-1}}    for allλ  &gt;  0{\lambda&gt;0}    under the assumptions that the potential  V  belongs to some integrable spaces and a spectral condition of  H  at zero is satisfied. As applications, we establish a sharp Hörmander-type spectral multiplier theorem associated with Schrödinger operators  H  and deduceL  p{L^{p}}   -bounds of the corresponding Bochner–Riesz operators. Next, we consider the fractional Schrödinger operatorH  =(   -  Δ   )   α   +  V{H=(-\Delta)^{\alpha}+V}    (0  &lt;   2  ⁢  α   &lt;  n{0&lt;2\alpha&lt;n}   ) and prove a uniform Hardy–Littlewood–Sobolev inequality for(   -  Δ   )   α{(-\Delta)^{\alpha}}   , which generalizes the corresponding result of Kenig–Ruiz–Sogge [ 20 ].

Remarks on L p -limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems