TY - JOUR

T1 - Inner functions on spaces of homogeneous type

AU - Александров, Алексей Борисович

PY - 1984/10

Y1 - 1984/10

N2 - 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[Figure not available: see fulltext.], such that the function ∇u is bounded in B and |∇u| =H almost everywhere on S.

AB - 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[Figure not available: see fulltext.], such that the function ∇u is bounded in B and |∇u| =H almost everywhere on S.

UR - http://www.scopus.com/inward/record.url?scp=34250139782&partnerID=8YFLogxK

U2 - 10.1007/BF01474134

DO - 10.1007/BF01474134

M3 - Article

AN - SCOPUS:34250139782

VL - 27

SP - 2433

EP - 2437

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -