Vertical Littlewood–Paley functions related to a Schrödinger operator
DOI:
https://doi.org/10.33044/revuma.4381Abstract
In this work we consider the Littlewood–Paley quadratic function associated to the Schrödinger operator $\mathcal{L}= -\Delta+V$ involving spatial derivatives of the semigroup's kernel. Under an appropriate reverse-Hölder condition on the potential we show boundedness on weighted $L^p$ spaces for $1 < p < p_0$, where $p_0$ depends on the order of the reverse-Hölder property. Using a subordination formula we extend these results to the corresponding quadratic function associated to the semigroup related to $\mathcal{L}^\alpha$, $0 < \alpha < 1$.
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