This article is cited in 3 papers

Behavior of a singular integral with the Hilbert kernel near a point of weak continuity of its density

R. B. Salimov

Chair of Higher Mathematics, Kazan State Architecture and Building University, Kazan, 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 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: 517.54

Received: 19.03.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:6, 32–38

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