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- Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-morrey spacesPublication . Deringoz, Fatih; Guliyev, Vagif S.; Samko, StefanWe prove the boundedness of the Hardy-Littlewood maximal operator and their commutators with BMO-coefficients in vanishing generalized Orlicz-Morrey spaces VM Phi,phi(R-n) including weak versions of these spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators involving the Young function Phi(u) and the function phi(x, r) defining the space. No kind of monotonicity condition on phi(x, r) in r is imposed.
- A class of Hausdorff-Berezin operators on the unit discPublication . Karapetyants, Alexey; Samko, Stefan; Zhu, KeheWe introduce and study a class of Hausdorff-Berezin operators on the unit disc based on Haar measure (that is, the Mobius invariant area measure). We discuss certain algebraic properties of these operators and obtain boundedness conditions for them. We also reformulate the obtained results in terms of ordinary area measure.