Functional Analysis and Applications Seminar 

21/05/2010, 15:15 — 16:00 — Room P3.10, Mathematics Building
Natasha Samko, Universidade do Algarve, Faro

Off-diagonal estimations of Hardy and potential operators in Morrey spaces

We study the weighted \(p\to q\)-boundedness of multi-dimensional Hardy type operators in Morrey spaces for a class of almost monotonic weights. The obtained results are applied to a similar weighted \(p\to q\)-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.