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Weighted Hardy and singular operators in Morrey spaces. (English) Zbl 1155.42005
In the interesting paper under review, the author studies the weighted boundedness of the Cauchy singular integral operator S Γ in the framework of the Morrey spaces p,λ (Γ) on curves satisfying the arc-chord condition, for a class of “radial type” almost monotonic weights. The non-weighted boundedness is shown to hold over an arbitrary Carleson curve, while the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces p,λ (0,),>0· Conditions are found for the weighted Hardy operators in order to be bounded in Morrey spaces. To cover the case of curves, the author extends the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves.
MSC:
42B20Singular and oscillatory integrals, several variables
42B25Maximal functions, Littlewood-Paley theory
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