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

2010/02/25 by Alexei Yu. Karlovich, Karlovich, Alexei Yu.
Mathematics · #42B25 #46E30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary 47B35 #Secondary 42B20 #math.CA #math.FA #msc:42B20 #msc:42B25 #msc:46E30 #msc:47B35

paper · pdf · doi:10.48550/arxiv.1002.4813

23 pages

arxiv created 2010/02/25 · openalex publication_date 2010/02/25 · arxiv updated 2010/02/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

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.

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