Wavelet decomposition of harmonic functions in growth spaces
  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. 
Kjersti Solberg Eikrem, Eugenia Malinnikova, Pavel A. Mozolyako
math.FA math.CV