Boundary behavior of monotone Sobolev functions on John domains in a metric space. (English) Zbl 1074.31005

The authors study weighted boundary limits of monotone Sobolev functions on bounded \((\eta,\varphi)\)-John domains in a metric space. The result obtained in the paper extends some results by the second author [Hiroshima Math. J. 18, No. 1, 207–217 (1988; Zbl 0664.31007), Ann. Inst. Fourier 40, No. 4, 811–833 (1990; Zbl 0715.31002), Complex Variables, Theory Appl. 27, No. 2, 117–131 (1995; Zbl 0845.31002), Ann. Acad. Sci. Fenn., Ser. A I, Math. 20, No. 2, 315–326 (1995; Zbl 0852.31008)] for harmonic functions, polyharmonic functions and monotone functions on the upper half space \(\mathbb{R}^n_+\).


31B25 Boundary behavior of harmonic functions in higher dimensions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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