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Compactness of Commutators of One-Sided Singular Integrals in Weighted Lebesgue Spaces

Part of: Inequalities Harmonic analysis in several variables

Published online by Cambridge University Press:  10 January 2019

Víctor García García  and
Pedro Ortega Salvador
Víctor García García
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071, Málaga, Spain (victorgarcia2@uma.es; portega@uma.es)
Pedro Ortega Salvador
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071, Málaga, Spain (victorgarcia2@uma.es; portega@uma.es)
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Abstract

We prove that if p > 1, $w\in A_p^ +$, b ∈ CMO and $C_b^ + $ is the commutator with symbol b of a Calderón–Zygmund convolution singular integral with kernel supported on (−∞, 0), then $C_b^ + $ is compact from Lp(w) into itself.

Keywords

commutatorscompact operatorscompactnessweights

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 655 - 665
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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