Geodesic
New asymptotic representation of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 73-78

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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 module of the logarithm of the distance from this point to a variable one, and the integral is not necessarily convergent.
Keywords: singular integral, Hölder condition, weak continuity.
Mots-clés : Hilbert kernel 
@article{IVM_2016_4_a8,
     author = {R. B. Salimov},
     title = {New asymptotic representation of a~singular integral with the {Hilbert} kernel near a~point of weak continuity of its density},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--78},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_4_a8/}
}
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R. B. Salimov. New asymptotic representation of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 73-78. http://geodesic.mathdoc.fr/item/IVM_2016_4_a8/