Geodesic
Generalized Hölder type spaces of harmonic functions in the unit ball and half space
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 675-691 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity $\omega =\omega (h)$ and the second is the variable exponent harmonic Hölder space with the continuity modulus $|h|^{\lambda (\cdot )}$. We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.
We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity $\omega =\omega (h)$ and the second is the variable exponent harmonic Hölder space with the continuity modulus $|h|^{\lambda (\cdot )}$. We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.
DOI : 10.21136/CMJ.2019.0431-18
Classification : 42B35, 46E15, 46E30
Keywords: Hölder space; harmonic function; variable exponent space; modulus of continuity 
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     title = {Generalized {H\"older} type spaces of harmonic functions in the unit ball and half space},
     journal = {Czechoslovak Mathematical Journal},
     pages = {675--691},
     year = {2020},
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     number = {3},
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Karapetyants, Alexey; Restrepo, Joel Esteban. Generalized Hölder type spaces of harmonic functions in the unit ball and half space. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 675-691. doi: 10.21136/CMJ.2019.0431-18

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