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arXiv · 2401.04010

Weighted inequalities for Schr\"odinger type Singular Integrals on variable Lebesgue spaces

Adrián Cabral
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Abstract

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 $\mathcal{L}$.

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Adrián Cabral. 2024-01-08. Weighted inequalities for Schr\"odinger type Singular Integrals on variable Lebesgue spaces. https://doi.org/10.2140/tunis.2024.6.321

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