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Inner functions on spaces of homogeneous type

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Abstract

One shows that the methods of M. Hakim, N. Sibony, and E. Løw, used by them for the construction of inner functions in a sphere, can be applied also in a more general situation. The fundamental result of the paper is: For any positive continuous function H on the unit sphere S of the space ℝd, there exists a real function u, harmonic in the unit ball

, such that the function ∇u is bounded in B and ¦∇u¦ =H almost everywhere on S.

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Authors
  1. A. B. Aleksandrov
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 7–14, 1983.

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Aleksandrov, A.B. Inner functions on spaces of homogeneous type. J Math Sci 27, 2433–2437 (1984). https://doi.org/10.1007/BF01474134

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  • DOI: https://doi.org/10.1007/BF01474134

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