Geodesic
$L_p$-versions of one conformally invariant inequality
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 88-92

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We obtain $L_p$ versions of theorems proved by J. L. Fernández, J. M. Rodríguez in The exponent of convergence of Riemann surfaces, bass Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A. I. Mathematica 15, 165–182 (1990). An important role in the proof of our results is approach of V. M. Miklyukov and M. K. Vuorinen. We use the isoperimetric profile of hyperbolic domains.
Keywords: Poincaré metric, isoperimetric inequality, uniformly perfect set, Hardy type inequality. 
@article{IVM_2018_8_a10,
     author = {F. G. Avkhadiev and R. G. Nasibullin and I. K. Shafigullin},
     title = {$L_p$-versions of one conformally invariant inequality},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {88--92},
     publisher = {mathdoc},
     number = {8},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_8_a10/}
}
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F. G. Avkhadiev; R. G. Nasibullin; I. K. Shafigullin. $L_p$-versions of one conformally invariant inequality. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 88-92. http://geodesic.mathdoc.fr/item/IVM_2018_8_a10/