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Weighted inequalities for Schrödinger type singular integrals on variable Lebesgue spaces

Adrián Cabral

Vol. 6 (2024), No. 2, 321–342
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 = Δ + V in d, where d > 2 and the nonnegative potential V belongs to the reverse Hölder class RH q with q > d2. 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 .

Keywords
Schrödinger operator, singular integrals, variable Lebesgue spaces, weights
Mathematical Subject Classification
Primary: 42B20, 42B35
Secondary: 35J10
Milestones
Received: 28 August 2023
Revised: 26 December 2023
Accepted: 11 January 2024
Published: 29 June 2024
Authors
Adrián Cabral
Facultad de Ciencias Exactas y Naturales y Agrimensura
Universidad Nacional del Nordeste
Corrientes
Argentina