Abstract:
Under study is the class of ring $Q$-homeomorphisms with respect to the $p$-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.
Keywords:$p$-modulus, $p$-capacity, $Q$-homeomorphism, ring $Q$-homeomorphism, quasiconformal mapping, mean quasiconformal mapping.
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