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Weighted Hardy and potential operators in the generalized Morrey spaces. (English) Zbl 1211.42018
The authors study the weighted pq-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces p,ϕ ( n ,w) defined by an almost increasing function ϕ(r) and radial type weight w(|x|) from the Bary-Stechkin-type class. Sufficient conditions are obtained, in terms of some integral inequalities imposed on ϕ and w, for such a pq-boundedness. In the case of local spaces the obtained conditions are also necessary. These results are applied to derive a similar weighted pq-boundedness of the Riesz potential operator.
42B25Maximal functions, Littlewood-Paley theory
47B38Operators on function spaces (general)
47G40Potential operators
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