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On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in \(R^ n\). (English) Zbl 0658.31006
The orthogonal projection of a square summable function in Lebesgue’s sense, defined in \(D\subset R_ n\), D bounded, into the space of square summable harmonic functions, defined in D, is studied in the paper. If D is the unit ball, the reproducing kernel of the projection operator has a more practical form than in the general case. By means of the reproducing kernel, the author studies the properties of Bloch’s harmonic functions space and of the Sobolev and Hölder spaces of harmonic functions. Using the interpolation property of Bloch’s harmonic functions, he studies also the properties of weighted Sobolev spaces of harmonic functions.
Reviewer: V.Ionescu

MSC:
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
26B40 Representation and superposition of functions
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