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Wavelet expansions for weighted, vector-valued BMO functions

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Abstract

We introduce a scale of weighted Carleson norms, which depend on an integrability parameter p, where p = 2 corresponds to the classical Carleson measure condition. Relations between the weighted BMO norm of a vector-valued function f: ℝ → X, and the Carleson norm of the sequence of its wavelet coefficients, are established. These extend the results of Harboure-Salinas-Viviani, also in the scalar-valued case when p ≠ 2.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin Katu 2B, FI-00014, Helsinki, Finland

    Tuomas Hytönen

  2. Instituto de Matemática Aplicada Del Litoral, Güemes 3450, 3000, Santa Fe, República, Argentina

    Oscar Salinas & Beatriz Viviani

Authors
  1. Tuomas Hytönen
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  2. Oscar Salinas
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  3. Beatriz Viviani
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Correspondence to Tuomas Hytönen.

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Hytönen, T., Salinas, O. & Viviani, B. Wavelet expansions for weighted, vector-valued BMO functions. JAMA 111, 321–337 (2010). https://doi.org/10.1007/s11854-010-0020-5

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  • DOI: https://doi.org/10.1007/s11854-010-0020-5

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