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arXiv:1203.5290 [math.FA]AbstractReferencesReviewsResources

Wavelet decomposition of harmonic functions in growth spaces

Kjersti Solberg Eikrem, Eugenia Malinnikova, Pavel A. Mozolyako

Published 2012-03-23, updated 2013-01-30Version 2

Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of harmonic functions along vertical lines.

Comments: 18 pages
Journal: Journal d'Analyse Math\'ematique, 122 (2014), 87-111
Categories: math.FA, math.CV
Subjects: 31B25, 42C40, 60G46
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