arXiv subjects

Adrián Cabral

Publications and source records attributed to Adrián Cabral.

2 recordsLinked to original sources

arXiv2024

Weighted inequalities for Schrödinger type Singular Integrals on variable Lebesgue spaces

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 $\mathcal{L}=-Δ+V$ in $\mathbb{R}^d$, where $d>2$ and the non-negative potential $V$ belongs to the reverse Hölder 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 $ρ$ which comes appears naturally in the harmonic analysis related to Schrödinger operator $\mathcal{L}$.

math.AP↗

arXiv2022

Weighted norm inequalities for the maximal functions associated to a critical radius function on variable Lebesgue spaces

In this work we obtain boundedness on weighted variable Lebesgue spaces of some maximal functions that come from the localized analysis considering a critical radius function. This analysis appears naturally in the context of the Schrödinger operator $\mathcal{L}=-Δ+V$ in $\mathbb{R}^d$, where $V$ a non-negative potential satisfying some specific reverse Hölder condition. We consider new classes of weights that locally behave as the Muckenhoupt class for Lebesgue spaces with variable exponents considered in Cruz Uribe et al. (J. Math. Anal. Appl. 394(2):744-760, 2012) and actually include them.

math.CA↗