## Harmonic majorization and thinness.(English)Zbl 0637.31002

Abstract analysis, Proc. 14th Winter Sch., Srní/Czech. 1986, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 14, 295-304 (1987).
[For the entire collection see Zbl 0627.00012.]
The author describes some results about existence of harmonic majorants for certain functions in domains in $${\mathbb{R}}^ d$$ which he has proved in several recent papers. For example, if D is a subdomain of the half-space $$x_ 1>0$$ and $$1<p<\infty$$, then $$| x|^ p$$ has a harmonic majorant in D if and only if $$x^ p_ 1$$ does.
Reviewer: A.Baernstein II

### MSC:

 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions

### Keywords:

thinness; existence; harmonic majorants

Zbl 0627.00012
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