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Journal of Function Spaces and Applications
Volume 2012, Article ID 678171, 21 pages
Research Article

Weighted Hardy and Potential Operators in Morrey Spaces

Department of Mathematics, Research Center CEAF, Instituto Superior Técnico, 1049-003 Lisbon, Portugal

Received 15 November 2009; Accepted 9 June 2010

Academic Editor: V. Stepanov

Copyright © 2012 Natasha Samko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the weighted pq-boundedness of Hardy-type operators in Morrey spaces p,λ(n) (or p,λ(+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weighted pq-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.