This article is cited in 4 papers

Brief communications

The behavior of a singular integral with the Hilbert kernel near a point where the density of the integral is weakly continuous

R. B. Salimov

Chair of Higher Mathematics, Kazan State University of Architecture and Engineering, Kazan, Russia

Abstract: We study the behavior of a singular integral with the Hilbert kernel near a point where the continuous density of the integral does not satisfy the Hölder condition and, as a result, the integral, possibly, diverges.

Keywords: singular integral, Hilbert kernel, weak continuity.

UDC: 517.544

Received: 27.10.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:6, 52–56

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