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New asymptotic representation for singular integral with Hilbert kernel near a point of weak continuity of density

Authors
  • Salimov, R. B.1
  • 1 Kazan State Architecture and Civil Engineering University, ul. Zelyonaya 1, Kazan, 420043, Russia , Kazan (Russia)
Type
Published Article
Journal
Russian Mathematics
Publisher
Allerton Press
Publication Date
Apr 01, 2016
Volume
60
Issue
4
Pages
60–64
Identifiers
DOI: 10.3103/S1066369X16040095
Source
Springer Nature
Keywords
License
Yellow

Abstract

We obtain an asymptotic representation of singular integral with the Hilbert kernel near a point, where modulus of continuity of its density behaves itself as inverse value of double logarithm of distance from this point.

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