This article is cited in 1 paper

Asymptotical representation of singular integral with the Hilbert kernel near a point of weak continuity of density

R. B. Salimov

Chair of Higher Mathematics, Kazan State Architecture and Building University, 1 Zelyonaya str., Kazan, 420043 Russia

Abstract: We derive asymptotical representation of singular integral with the Hilbert kernel near a fixed point at which an integral density vanishes as a negative power of module of logarithm of a distance from variable point to a fixed one.

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

UDC: 517.54

Received: 14.10.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:7, 52–55

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