On the properties of a Riesz potential with oscillating kernel

On the properties of a Riesz potential with oscillating kernel

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.

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Veröffentlicht in:Siberian mathematical journal 2014-03, Vol.55 (2), p.201-209
1. Verfasser: Arbuzov, È. V.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446614020025