Singular Integral Operators on Variable Lebesgue Spaces over Arbitrary Carleson Curves

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dc.creatorKarlovich, Alexei Yu.
dc.date2008-10-17
dc.date.accessioned2026-07-07T10:10:57Z
dc.date.available2026-07-07T10:10:57Z
dc.descriptionIn 1968, Israel Gohberg and Naum Krupnik discovered that local spectra of singular integral operators with piecewise continuous coefficients on Lebesgue spaces $L^p(Γ)$ over Lyapunov curves have the shape of circular arcs. About 25 years later, Albrecht Böttcher and Yuri Karlovich realized that these circular arcs metamorphose to so-called logarithmic leaves with a median separating point when Lyapunov curves metamorphose to arbitrary Carleson curves. We show that this result remains valid in a more general setting of variable Lebesgue spaces $L^{p(\cdot)}(Γ)$ where $p:Γ\to(1,\infty)$ satisfies the Dini-Lipschitz condition. One of the main ingredients of the proof is a new sufficient condition for the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with weights related to oscillations of Carleson curves.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0810.3110
dc.identifierhttp://arxiv.org/abs/0810.3110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171745
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subject47B35
dc.titleSingular Integral Operators on Variable Lebesgue Spaces over Arbitrary Carleson Curves
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