Critical points of essential norms of singular integral operators in weighted spaces

Naum Krupnik, Yafim Spigel

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We show that for any simple piecewise Ljapunov contour Γ there exists a power weight ρ such that the essential norm |SΓ| in the space L2(Γ, ρ) does not depend on the angles of the contour and it is given by formula (2). All such weights are described. For the union Γ = Γ1 ∪ Γ2 of two simple piecewise Lyapunov curves we prove that the essential norm |SΓ| in L2(Γ) is minimal if both Γ1 and Γ2 are smooth in some neighborhoods of the common points. It is the case when the norm |SΓ| in the space L2(Γ) as well as in Z2(Γ, p) does not depend on the values of the angles and it can be calculated by formula (5).

Original languageEnglish
Pages (from-to)211-220
Number of pages10
JournalIntegral Equations and Operator Theory
Volume33
Issue number2
DOIs
StatePublished - 1999

Bibliographical note

Funding Information:
1 This research was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humarrities.

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