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

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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.

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Authors and Affiliations

  1. Kazan State University of Architecture and Engineering, ul. Zelyonaya 1, Kazan, 420043, Russia

    R. B. Salimov

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  1. R. B. Salimov
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Original Russian Text © R.B. Salimov, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 6, pp. 61–66.

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Salimov, R.B. The behavior of a singular integral with the Hilbert kernel near a point where the density of the integral is weakly continuous. Russ Math. 56, 52–56 (2012). https://doi.org/10.3103/S1066369X12060072

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  • DOI: https://doi.org/10.3103/S1066369X12060072

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