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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 2, Pages 251–260 (Mi smj2529)  
On the properties of a Riesz potential with oscillating kernel

È. V. Arbuzov

Sobolev Institute of Mathematics, Novosibirsk, Russia
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Abstract: We consider a potential-type integral operator with oscillating kernel in the space of functions representable as Riesz potentials. We obtain estimates of its norm in the Lebesgue spaces which depend on the oscillation parameter to a negative power.
Keywords: potential-type integral operator, Riesz fractional derivative.
Received: 26.09.2013
English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 2, Pages 201–209
DOI: https://doi.org/10.1134/S0037446614020025
Bibliographic databases:
Document Type: Article
UDC: 517.518.12
Language: Russian
Citation: È. V. Arbuzov, “On the properties of a Riesz potential with oscillating kernel”, Sibirsk. Mat. Zh., 55:2 (2014), 251–260; Siberian Math. J., 55:2 (2014), 201–209
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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