Geodesic
A Hardy-type inequality and its applications
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 112-132.

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We prove a Hardy-type inequality that provides a lower bound for the integral $\int_0^\infty|f(r)|^pr^{p-1}\,dr$, $p>1$. In the scale of classical Hardy inequalities, this integral corresponds to the value of the exponential parameter for which neither direct nor inverse Hardy inequalities hold. However, the problem of estimating this integral and its multidimensional generalization from below arises in some practical questions. These are, for example, the question of solvability of elliptic equations in the scale of Sobolev spaces in the whole Euclidean space $\mathbb R^n$, some questions in the theory of Sobolev spaces, hydrodynamic problems, etc. These questions are studied in the present paper. 
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Yu. A. Dubinskii. A Hardy-type inequality and its applications. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 112-132. http://geodesic.mathdoc.fr/item/TM_2010_269_a8/

[1] Khardi G.G., Littlvud Dzh.E., Polia G., Neravenstva, Izd-vo inostr. lit., M., 1948

[2] Kufner A., Maligranda L., Persson L.-E., The Hardy inequality: About its history and some related results, Vydavatelský Serv., Pilsen, 2007 | MR | Zbl

[3] Temam R., Uravneniya Nave–Stoksa: Teoriya i chislennyi analiz, Mir, M., 1981 | MR | Zbl

[4] Smirnov V.I., Kurs vysshei matematiki, v. 5, Fizmatgiz, M., 1959 | MR

[5] Dubinskii Yu.A., “Razlozheniya sobolevskoi shkaly i gradientno-divergentnoi shkaly v summu solenoidalnykh i potentsialnykh podprostranstv”, Tr. MIAN, 255, 2006, 136–145 | MR

[6] Borovikov I.A., Dubinskii Yu.A., “Nekotorye razlozheniya modulei Soboleva–Klifforda i nelineinye variatsionnye zadachi”, Tr. MIAN, 260, 2008, 57–74 | MR | Zbl

[7] Dubinskii Yu.A., “Neravenstva Khardi pri isklyuchitelnykh znacheniyakh parametrov i ikh prilozheniya”, DAN, 427:5 (2009), 586–590 | MR | Zbl