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Integral representations of harmonic functions in half spaces. (English) Zbl 1111.31002
The author gives an integral formula for a harmonic function in the upper half-space in the case when its positive part satisfies a slow growth condition.

MSC:
31A05Harmonic, subharmonic, superharmonic functions (two-dimensional)
31A10Integral representations of harmonic functions (two-dimensional)
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Full Text: DOI
References:
[1] Axler, S.; Bourdon, P.; Ramey, W.: Harmonic function theory. (1992) · Zbl 0765.31001
[2] Gilbarg, D.; Trudinger, N.: Elliptic partial differential equations of second order. (2001) · Zbl 1042.35002
[3] Groemer, H.: Geometric applications of Fourier series and spherical harmonics. Encyclopedia of mathematics and its applications 61 (1996) · Zbl 0877.52002
[4] Hörmander, L.: Notions of convexity. (1994) · Zbl 0835.32001
[5] Stein, E. M.: Harmonic analysis. (1993) · Zbl 0821.42001
[6] Stein, E. M.; Weiss, G.: Introduction to Fourier analysis on Euclidean space. (1971) · Zbl 0232.42007