TWO-WEIGHTED ESTIMATES OF RIEMANN-LIOUVILLE INTEGRALS

Abstract

Weighted estimates (1)are considered, where the constant does not depend on , for fractional Riemann- Liouville integrals and the following problem is examined: find necessary and sufficient conditions on weight functions and under which estimate (1) is valid for all functions for which the right-hand side of (1) is finite. The problem is solved for and . This result is definitive, and it generalizes known results for integral operators when . Bibliography: 19 titles.