Characterization of weighted spaces of Riesz potentials via approximative inverse operators
by
Stefan Samko
Universidade do Algarve, Portugal
Coauthors: Vladimir A. Nogin (Rostov State University, Russia)

The weighted space I^\alpha[L_p(\rho)] is considered, where I^\alpha is the Riesz potential operator and \rho(x) is a Muckenhoupt-Wheeden A_{p, q}-weight function. A family of operators D^\alpha_\epsilon, approximatively left inverse to I\alpha is constructed and in terms of convergence of the operators D^\alpha_\epsilon there is given a criterion for a function to belong to the space I^\alpha[L_p(\rho)].

http://w3.ualg.pt/~ssamko/

Date received: April 22, 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 # cahk-05.