Criteria for the Boundedness and Compactness of Generalized One-Sided Potentials

Abstract

Necessary and sufficient conditions are found for the positive Borel measure $\nu$, which provide the boundedness (compactness) of the generalized Riemann--Liouville operator from one Lebesgue space into another Lebesgue space with measure $\nu$. The appropriate problem for the generalized Weyl operator is solved as well.