@inbook{539502fea44d4e4f9ea5c17a74c1ee75,

title = "Maximal Noncompactness of Singular Integral Operators on L2 Spaces with Some Khvedelidze Weights",

abstract = "Let Γ be a contour in the complex plane consisting of a finite number of circular arcs joining the endpoints −1 and 1, possibly including the segment [−1,1]. We consider the singular integral operator A=aI+bSΓ with constant coefficients a,b∈ℂ, where SΓ is the Cauchy singular integral operator over Γ. We provide a detailed proof of the maximal noncompactness of the operator A on L2 spaces with the Khvedelidze weights ϱ(t)=|t−1|β|t+1|−β satisfying −1<β<1. This result was announced by Naum Krupnik in 2010, but its proof has never been published.",

keywords = "Cauchy singular integral operator, Essential norm, Khvedelidze weight, Maximal noncompactness, Norm",

author = "Oleksiy Karlovych and Alina Shalukhina",

note = "Funding Information: This work is funded by national funds through the FCT Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The second author is funded by national funds through the FCT Funda{\c c}{\~a}o para a Ciencia e a Tecnologia, I.P., under the scope of the PhD scholarship UI/BD/154284/2022. Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.",

year = "2024",

doi = "10.1007/978-3-031-50613-0_12",

language = "English",

isbn = "978-3-031-50615-4",

series = "Operator Theory: Advances and Applications",

publisher = "Springer",

pages = "279--295",

editor = "Marek Ptak and Woerdeman, {Hugo J.} and Micha{\l} Wojtylak",

booktitle = "Operator and Matrix Theory, Function Spaces, and Applications",

address = "Netherlands",

}