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Wavelet characterization of growth spaces of harmonic functions

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway

    Kjersti Solberg Eikrem & Eugenia Malinnikova

  2. Department of Mathematics and Mechanics and Chebyshev Laboratory, St. Petersburg State University, 198904, St. Petersburg, Russia

    Pavel A. Mozolyako

Authors
  1. Kjersti Solberg Eikrem
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  2. Eugenia Malinnikova
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  3. Pavel A. Mozolyako
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Corresponding author

Correspondence to Kjersti Solberg Eikrem.

Additional information

E. Malinnikova was supported by the Research Council of Norway, grants 185359/V30 and 213638.

P. A. Mozolyako was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St Petersburg State University) under RF government grant 11.G34.31.0026, and by RFBR grant 12-01-31492.

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Eikrem, K.S., Malinnikova, E. & Mozolyako, P.A. Wavelet characterization of growth spaces of harmonic functions. JAMA 122, 87–111 (2014). https://doi.org/10.1007/s11854-014-0004-y

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  • DOI: https://doi.org/10.1007/s11854-014-0004-y

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