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Fractional Calculus and Applied Analysis

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Volume 21, Issue 3

Issues

The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces

Estefanía Dalmasso
  • Instituto de Matemática Aplicada del Litoral, UNL, CONICET, FIQ Predio Dr. Alberto Cassano del CCT-CONICET-Santa Fe Colectora Ruta Nacional N o168, Santa Fe, Argentina
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/ Gladis Pradolini / Wilfredo Ramos
Published Online: 2018-07-12 | DOI: https://doi.org/10.1515/fca-2018-0034

Abstract

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including Lp-Lq, Lp-BMO and Lp-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander’s type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p.

MSC 2010: Primary 42B25; Secondary 42B35

Key Words and Phrases: fractional calculus operators; commutators; Lipschitz symbols; weights

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About the article

Received: 2017-03-03

Published Online: 2018-07-12

Published in Print: 2018-06-26


Citation Information: Fractional Calculus and Applied Analysis, Volume 21, Issue 3, Pages 628–653, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2018-0034.

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