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Localization of a Class of Muckenhoupt Weights by Using Mellin Pseudo-Differential Operators

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Advances in Microlocal and Time-Frequency Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Let Γ be a finite or infinite interval of \(\mathbb R\), p ∈ (1, ∞), and let w ∈ A p( Γ) be a Muckenhoupt weight. Relations of the weighted singular integral operator \(wS_{\mathbb{R}_+}w^{-1}I\) on the space \(L^p(\mathbb{R}_{+})\) and Mellin pseudo-differential operators with non-regular symbols are studied. A localization of a class of Muckenhoupt weights to power weights at finite endpoints of Γ, which is related to the Allan-Douglas local principle, is obtained by using quasicontinuous functions and Mellin pseudo-differential operators with non-regular symbols.

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Authors and Affiliations

  1. Centro de Investigación en Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, Mexico

    Yu. I. Karlovich

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  1. Yu. I. Karlovich
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Correspondence to Yu. I. Karlovich .

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Editors and Affiliations

  1. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Paolo Boggiatto

  2. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Marco Cappiello

  3. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Elena Cordero

  4. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Sandro Coriasco

  5. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Gianluca Garello

  6. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Alessandro Oliaro

  7. Dipartimento di Matematica "G. Peano", Università degli Studi di Torino, Torino, Italy

    Jörg Seiler

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Karlovich, Y.I. (2020). Localization of a Class of Muckenhoupt Weights by Using Mellin Pseudo-Differential Operators. In: Boggiatto, P., et al. Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36138-9_17

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