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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
Article

Abstract

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.

Keywords

Harmonic Function Bergman Space Lipschitz Domain Iterate Logarithm Multiresolution Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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