Fredholmness of Singular Integral Operators with Complex Conjugation on Star-Like Curves with Cusps

The paper is devoted to studying the Fredholmness of operators from the Banach algebra B of singular integral operators with complex conjugation and slowly oscillating coefficients on the Lebesgue spaces L p ( Γ ) with p ∈ ( 1 , ∞ ) over star-like curves Γ with cusps. Applying reductions to a Banach...

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Bibliographic Details
Published in:Complex analysis and operator theory 2023-07, Vol.17 (5), Article 69
Main Authors: Karlovich, Yuri I., Monsiváis-González, Francisco J.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Banach spaces
Calculus
Coefficients
Conjugation
Cusps
Mathematical analysis
Mathematics
Mathematics and Statistics
Operator Theory
Operators (mathematics)
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Summary:The paper is devoted to studying the Fredholmness of operators from the Banach algebra B of singular integral operators with complex conjugation and slowly oscillating coefficients on the Lebesgue spaces L p ( Γ ) with p ∈ ( 1 , ∞ ) over star-like curves Γ with cusps. Applying reductions to a Banach algebra of Wiener–Hopf operators with slowly oscillating coefficients on weighted Lebesgue spaces over the half-line R + and a Banach algebra of convolution type operators with piecewise slowly oscillating coefficients on weighted Lebesgue spaces over the real line R , we construct a Fredholm symbol calculus for the Banach algebra B and establish a Fredholm criterion for the operators in B .
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-023-01375-3