This article is cited in 1 paper

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

R. B. Salimov

Kazan State Architecture and Civil Engineering University, 1 Zelyonaya str., Kazan, 420043, Russia

Abstract: We study the behavior of a singular integral with the Hilbert kernel near a fixed point, where the density vanishes as the value inverse to the logarithm of the module of the logarithm of the distance from this point to a variable one, and the integral is not necessarily convergent.

Keywords: singular integral, Hilbert kernel, Hölder condition, weak continuity.

UDC: 517.544

Received: 01.10.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:4, 60–64

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