Geodesic
Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces
Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 32-53

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The problem of the boundedness of a Calderon-Zygmund singular integral operator $T$ in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted $L_p$-spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for the boundedness of $T$ in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, for a genuine Calderon-Zygmund singular integral operator these sufficient conditions coincide with the necessary ones. 
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     title = {Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local {Morrey-type} spaces},
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V. I. Burenkov; V. S. Guliyev; A. Serbetci; T. V. Tararykova. Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces. Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 32-53. http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a5/