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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 $\omega =\omega \left(h\right)$ and the second is the variable exponent harmonic Hölder space with the continuity modulus ${\left|h\right|}^{\lambda (·)}$. We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.