@inbook{1ec89792472140869cedc2a6f2936f52,
title = "Maximal Noncompactness of Singular Integral Operators on Lp Spaces with Power Weights",
abstract = "We consider the singular integral operator A=aI+bSΓ with constant coefficients a,b∈ℂ, where SΓ is the Cauchy singular integral operator over a curve Γ in the complex plane. We discuss two situations when the operator A is maximally noncompact on the space Lp(Γ,ϱ) with 1<p<∞ and a power weight ϱ, that is, when its norm is equal to its essential norm and to its Hausdorff measure of noncompactness. Our results extend two results by Naum Krupnik obtained in earlier 1980s and in 2010.",
keywords = "Cauchy singular integral operator, Essential norm, Hausdorff measure of noncompactness, Maximal noncompactness, Norm, Power weight",
author = "Oleksiy Karlovych and Alina Shalukhina",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024. This work is funded by national funds through the FCT\u2014Funda\u00E7\u00E3o para a eCnicia 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\u2014Funda\u00E7\u00E3o para a Ciencia e a Tecnologia, I.P., under the scope of the PhD scholarship UI/BD/154284/2022. ",
year = "2024",
month = aug,
day = "21",
doi = "10.1007/978-3-031-62894-8_9",
language = "English",
isbn = "978-3-031-62893-1",
series = "Trends in Mathematics",
publisher = "Springer",
pages = "87--97",
editor = "Roland Duduchava and Eugene Shargorodsky and George Tephnadze",
booktitle = "Tbilisi Analysis and PDE Seminar",
address = "Netherlands",
}