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Hölder Continuity of Homeomorphisms with Controlled Growth of Their Spherical Means

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Holon Institute of Technology, 52 Golomb St., P.O.B. 305, 5810201, Holon, Israel

    Anatoly Golberg

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska St., Kiev 4, 01601, Ukraine

    Ruslan Salimov

Authors
  1. Anatoly Golberg
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  2. Ruslan Salimov
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Correspondence to Anatoly Golberg.

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Communicated by Aurelian Gheondea.

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Golberg, A., Salimov, R. Hölder Continuity of Homeomorphisms with Controlled Growth of Their Spherical Means. Complex Anal. Oper. Theory 11, 1825–1838 (2017). https://doi.org/10.1007/s11785-016-0632-6

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  • DOI: https://doi.org/10.1007/s11785-016-0632-6

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