Weighted Hardy and Potential Operators in Morrey Spaces

We study the weighted p -> q-boundedness of Hardy-type operators in Morrey spaces L-p,L-lambda(R-n) (or L-p,L-lambda (R-+(1)) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weighted p -> q-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.