Geodesic
Hardy-Type Inequalities on Planar and Spatial Open Sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 8-18.

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Several Hardy-type inequalities with explicit constants are proved for compactly supported smooth functions on open sets in the Euclidean space $\mathbb R^n$. 
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F. G. Avkhadiev. Hardy-Type Inequalities on Planar and Spatial Open Sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 8-18. http://geodesic.mathdoc.fr/item/TM_2006_255_a1/

[1] Ahlfors L.V., Conformal invariants: Topics in geometric function theory, McGraw-Hill, New York, 1973. | MR | Zbl

[2] Avkhadiev F.G., “Reshenie obobschennoi zadachi Sen-Venana”, Mat. sb., 189:12 (1998), 3–12 | MR | Zbl

[3] Avkhadiev F.G., “Konformno invariantnye neravenstva matematicheskoi fiziki”, Naukoemkie tekhnologii, 5:4 (2004), 47–51 | MR

[4] Avkhadiev F.G., “Hardy type inequalities in higher dimensions with explicit estimate of constants”, Lobachevskii J. Math., 21 (2006), 3–31 | MR | Zbl

[5] Avkhadiev F.G., Wirths K.-J., A theorem of Teichmüller, uniformly perfect sets and punishing factors, Preprint, Tech. Univ. Braunschweig, 2005; http://www.iaa.tu-bs.de/wirths/preprints/teich.ps

[6] Bandle C., Flucher M., “Harmonic radius and concentration of energy; hyperbolic radius and Liouville's equations $\Delta U=e^U$ and $\Delta U=U^{\frac{n+2}{n-2}}$”, SIAM Rev., 38:2 (1996), 191–238 | DOI | MR | Zbl

[7] Beardon A.F., Pommerenke Ch., “The Poincaré metric of plane domains”, J. London Math. Soc. Ser. 2, 18 (1978), 475–483 | DOI | MR | Zbl

[8] Carleson L., Gamelin T.W., Complex dynamics, Springer, New York, 1993 | MR | Zbl

[9] Davies E.B., “A review of Hardy inequalities”, The Maz'ya anniversary collection, v. 2, Oper. Theory. Adv. and Appl., 110, Birkhäuser, Basel, 1999, 55–67 | MR | Zbl

[10] Fernández J.L., Rodríguez J.M., “The exponent of convergence of Riemann surfaces. Bass Riemann surfaces”, Ann. Acad. sci. Fenn. A.I: Math., 15 (1990), 165–182 | MR

[11] Garnett J.B., Marschall D.E., Harmonic measure, Cambridge Univ. Press, Cambridge, 2005 | MR | Zbl

[12] Hardy G.H., Littlewood J.E., Polya G., Inequalities, Cambridge Univ. Press, Cambridge, 1973

[13] Maz'ya V.G., Sobolev spaces, Springer, Berlin–New York, 1985 | MR

[14] Opic B., Kufner A., Hardy-type inequalities, Pitman Res. Notes Math., 219, Longman, Harlow, 1990 | MR | Zbl

[15] Osgood B.G., “Some properties of $f''/f'$ and the Poincaré metric”, Indiana Univ. Math. J., 31 (1982), 449–461 | DOI | MR | Zbl

[16] Pommerenke Ch., “Uniformly perfect sets and the Poincaré metric”, Arch. Math., 32 (1979), 192–199 | DOI | MR | Zbl