Proceedings of conferences

On properties of the Cauchy integral operator with oscillating kernel

E. V. Arbuzov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The Cauchy integral operator with oscillating kernel are considered on the space of functions represented by Riesz potentials. An estimate for their norm in the Lebesgue space is obtained. The estimate depends on negative power of the oscillation parameter.

Keywords: Cauchy integral operator, Riesz fractional derivatives.

UDC: 517.518.12

MSC: 31B10

Received February 1, 2013, published May 31, 2013