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

• Autorzy: Alexei Yu. Karlovich
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 143-166

Daty

wydano

2011

Twórcy

autor

Alexei Yu. Karlovich

• Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal

Identyfikatory

DOI

10.4064/bc92-0-10