Characterizations of H1ΔN (ℝn) and BMOΔN (ℝn) via weak factorizations and commutators

Ji Li*, Brett D. Wick

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)


    This paper provides a deeper study of the Hardy and BMO spaces associated to the Neumann Laplacian ΔN. For the Hardy space HΔN 1(ℝn) (which is a proper subspace of the classical Hardy space H1(ℝn)) we demonstrate that the space has equivalent norms in terms of Riesz transforms, maximal functions, atomic decompositions, and weak factorizations. While for the space BMOΔN (ℝn) (which contains the classical BMO(ℝn)) we prove that it can be characterized in terms of the action of the Riesz transforms associated to the Neumann Laplacian on L(ℝn) functions and in terms of the behavior of the commutator with the Riesz transforms. The results obtained extend many of the fundamental results known for H1(ℝn) and BMO(ℝn).

    Original languageEnglish
    Pages (from-to)5384-5416
    Number of pages33
    JournalJournal of Functional Analysis
    Issue number12
    Publication statusPublished - 2017


    • Neumann Laplacian
    • Riesz transforms
    • Commutator
    • Hardy and BMO spaces


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