On the properties of a Riesz potential with oscillating kernel

È. V. Arbuzov

Sobolev Institute of Mathematics, Novosibirsk, Russia

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.

UDC: 517.518.12

Received: 26.09.2013

 English version: Siberian Mathematical Journal, 2014, 55:2, 201–209

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