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June 2020 Two weighted inequalities for operators associated to a critical radius function
B. Bongioanni, E. Harboure, P. Quijano
Illinois J. Math. 64(2): 227-259 (June 2020). DOI: 10.1215/00192082-8360714

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.

Citation

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B. Bongioanni. E. Harboure. P. Quijano. "Two weighted inequalities for operators associated to a critical radius function." Illinois J. Math. 64 (2) 227 - 259, June 2020. https://doi.org/10.1215/00192082-8360714

Information

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

zbMATH: 07210958
MathSciNet: MR4092957
Digital Object Identifier: 10.1215/00192082-8360714

Subjects:
Primary: 42B20
Secondary: 35J10

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 2 • June 2020
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