On the inversion of potential type operators with kernels having singularities on a sphere
by
Enrique Ramirez de Arellano
Centro de Investigacion y de Estudios Avanzados del IPN
Coauthors: Alexey N. Karapetyants

The inversion problem for operators A_a^\alpha with symbols a(|\xi|)|\xi|^-\alphae^i|\xi| is considered in the framework of L_p spaces. It is assumed that 1 <= p <= \infty, Re  \alpha >= 0, and a(|\xi|) is a L₁-L₁ multiplier which satisfies some additional properties, depending on the case under consideration. We treat here the particular important nonelliptic case in which a(|\xi|) =/= 0 for \xi =/= 0, but in which a(|\xi|) may degenerate (i.e., a=0) at the origin and at infinity. We also consider the general case of non-ellipticity, when a(|\xi|) degenerates on an arbitrary set of zero measure in Rⁿ. Additionally, we give information on the action of the operators A_a^\alpha on L_p spaces.

Date received: July 14, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahv-71.