In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schr\"odinger operator $\mathcal{ L}=-\Delta+V$ in $\mathbb{ R}^d$, where $d>2$ and the non-negative potential $V$ belongs to the reverse H\"older class $RH_q$ with $q>d/2$. Each of the operators that we are going to deal with are singular integrals given by a kernel $K(x,y)$, which satisfies certain size and smoothness conditions in relation to a critical radius function $\rho$ which comes appears naturally in the harmonic analysis related to Schr\"odinger operator $\mathcal{ L}$.
Categories: math.AP