Singular integral operators on Nakano spaces with weights having finite sets of discontinuities

Volume 92 / 2011

Alexei Yu. Karlovich Banach Center Publications 92 (2011), 143-166 MSC: Primary 47B35; Secondary 42B20, 42B25, 46E30. DOI: 10.4064/bc92-0-10

Abstract

In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form $aP+bQ$, where $a,b$ are piecewise continuous functions and $P,Q$ are complementary projections associated to the Cauchy singular integral operator, acting on Lebesgue spaces over Lyapunov curves. We extend this result to the case of Nakano spaces (also known as variable Lebesgue spaces) with certain weights having finite sets of discontinuities on arbitrary Carleson curves.

Authors

  • Alexei Yu. KarlovichDepartamento de Matemática
    Faculdade de Ciências e Tecnologia
    Universidade Nova de Lisboa
    Quinta da Torre
    2829–516 Caparica, Portugal
    e-mail

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