Geodesic
A Proof of the Hardy-Littlewood Theorem on Fractional Integration and a Generalization
Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 31 .

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We give an elementary proof of the Hardy-Littlewood theorem and extend it to a class of smooth functions on the unit ball. As a special case we prove the validity of this theorem in the class of polyharmonic function.
Classification : 30D55 31B30
Keywords: Fractional integral, Integral means, Polyharmonic functions 
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     author = {Miroslav Pavlovi\'c},
     title = {A {Proof} of the {Hardy-Littlewood} {Theorem} on {Fractional} {Integration} and a {Generalization}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {31 },
     publisher = {mathdoc},
     volume = {_N_S_59},
     number = {73},
     year = {1996},
     zbl = {0944.31007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a3/}
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Miroslav Pavlović. A Proof of the Hardy-Littlewood Theorem on Fractional Integration and a Generalization. Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 31 . http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a3/