Geodesic
Sharp Estimates for the Norms of Hardy-Type Operators on the Cones of Quasimonotone Functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 115-143

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Order-sharp three-weight estimates are established for the norms of restrictions of generalized Hardy operators onto the cones of functions from Lebesgue spaces that are monotone on a positive half-axis. The necessary and sufficient conditions are obtained for the boundedness of the norms under minimal a priori assumptions about the measures involved in the definitions of Hardy operators and weighted Lebesgue spaces. The uniformity of the estimates with respect to the parameters of the problem is observed. 
@article{TM_2001_232_a11,
     author = {M. L. Gol'dman},
     title = {Sharp {Estimates} for the {Norms} of {Hardy-Type} {Operators} on the {Cones} of {Quasimonotone} {Functions}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {115--143},
     publisher = {mathdoc},
     volume = {232},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_232_a11/}
}
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M. L. Gol'dman. Sharp Estimates for the Norms of Hardy-Type Operators on the Cones of Quasimonotone Functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 115-143. http://geodesic.mathdoc.fr/item/TM_2001_232_a11/