Abstract

In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schrödinger operator $\mathcal{ℒ}=-\mathrm{\Delta }+V$ in ${ℝ}^d$, where $d>2$ and the nonnegative potential $V$ belongs to the reverse Hölder class ${\mathrm{RH}<!--FUNCTION\; APPLICATION-->}_q$ 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 Schrödinger operator $\mathcal{ℒ}$.

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