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We continue the study of homeomorphisms preserving integrally controlled weighted p-module of the ring domains. It was established earlier that under appropriate growth condition for the spherical mean of the… Click to show full abstract
We continue the study of homeomorphisms preserving integrally controlled weighted p-module of the ring domains. It was established earlier that under appropriate growth condition for the spherical mean of the weight such mappings are locally Hölder continuous with respect to logarithms of the distances. In this paper, we consider much more general growth conditions and derive the differentiability almost everywhere, local Lipschitz and Hölder continuity. The sharpness of these results is illustrated by several examples. The distortion estimates for measures under such mappings are also established.
Journal Title: Complex Analysis and Operator Theory
Year Published: 2017
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