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

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Abstract

We study properties of a singular integral with the Hilbert kernel at a fixed point, where the modulus of continuity of its density has logarithmic order, and the integral is not necessarily convergent.

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Authors and Affiliations

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

    R. B. Salimov

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  1. R. B. Salimov
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Correspondence to R. B. Salimov.

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Original Russian Text © R.B. Salimov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 6, pp. 37–44.

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Salimov, R.B. Behavior of a singular integral with Hilbert kernel at a point of weak continuity of its density. Russ Math. 57, 32–38 (2013). https://doi.org/10.3103/S1066369X13060042

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  • DOI: https://doi.org/10.3103/S1066369X13060042

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