Czechoslovak Mathematical Journal, Vol. 70, No. 3, pp. 675-691, 2020


Generalized Hölder type spaces of harmonic functions in the unit ball and half space

Alexey Karapetyants, Joel Esteban Restrepo

Received October 1, 2018.   Published online December 10, 2019.

Abstract:  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 $ømega=ømega(h)$ 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.
Keywords:  Hölder space; harmonic function; variable exponent space; modulus of continuity
Classification MSC:  42B35, 46E30, 46E15
DOI:  10.21136/CMJ.2019.0431-18

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Affiliations:   Alexey Karapetyants, Southern Federal University, Mathematics, Mechanics and Computer Sciences Department, Miltchakova 8a, Rostov-on-Don, 344090 Russia; and University at Albany, State University of New York, 1400 Washington Avenue Albany, NY 12222, USA, e-mail: karapetyants@gmail.com; Joel Esteban Restrepo (corresponding author), Regional Mathematical Center of Southern Federal University, Miltchakova 8a, Rostov-on-Don, 344090 Russia, e-mail: cocojoel89@yahoo.es


 
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