Harmonic majorization and thinness. (English) Zbl 0637.31002

Essén, Matts

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

Citations:

Zbl 0627.00012