Journal d'Analyse Mathématique

, Volume 122, Issue 1, pp 87–111 | Cite as

Wavelet characterization of growth spaces of harmonic functions

  • Kjersti Solberg Eikrem
  • Eugenia Malinnikova
  • Pavel A. Mozolyako


We consider the space h ν of harmonic functions in R + n+1 with finite norm ‖u ν = sup |u(x, t)|/v(t), where the weight ν satisfies the doubling condition. Boundary values of functions in h ν are characterized in terms of their smooth multiresolution approximations. The characterization yields the isomorphism of Banach spaces h ν l . The results are also applied to obtain the law of the iterated logarithm for the oscillation of functions in h ν along vertical lines.


Harmonic Function Bergman Space Lipschitz Domain Iterate Logarithm Multiresolution Analysis 
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Copyright information

© Hebrew University Magnes Press 2014

Authors and Affiliations

  • Kjersti Solberg Eikrem
    • 1
  • Eugenia Malinnikova
    • 1
  • Pavel A. Mozolyako
    • 2
  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of Mathematics and Mechanics and Chebyshev LaboratorySt. Petersburg State UniversitySt. PetersburgRussia

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