Illinois Journal of Mathematics

Two weighted inequalities for operators associated to a critical radius function

B. Bongioanni, E. Harboure, and P. Quijano

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Abstract

In the general framework of Rd equipped with Lebesgue measure and a critical radius function, we introduce several Hardy–Littlewood type maximal operators and related classes of weights. We prove appropriate two weighted inequalities for such operators as well as a version of Lerner’s inequality for a product of weights. With these tools we are able to prove factored weight inequalities for certain operators associated to the critical radius function. As it is known, the harmonic analysis arising from the Schrödinger operator L=Δ+V, as introduced by Shen, is based on the use of a related critical radius function. When our previous result is applied to this case, it allows to show some inequalities with factored weights for all first and second order Schrödinger–Riesz transforms.

Article information

Source
Illinois J. Math., Volume 64, Number 2 (2020), 227-259.

Dates
Received: 21 October 2019
Revised: 15 February 2020
First available in Project Euclid: 1 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1588298629

Digital Object Identifier
doi:10.1215/00192082-8360714

Mathematical Reviews number (MathSciNet)
MR4092957

Zentralblatt MATH identifier
07210958

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 35J10: Schrödinger operator [See also 35Pxx]

Citation

Bongioanni, B.; Harboure, E.; Quijano, P. Two weighted inequalities for operators associated to a critical radius function. Illinois J. Math. 64 (2020), no. 2, 227--259. doi:10.1215/00192082-8360714. https://projecteuclid.org/euclid.ijm/1588298629


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