VMO spaces associated with operators with Gaussian upper bounds on product domains

The Anh Bui, Xuan Thinh Duong, Ji Li*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    In this paper, we extend the well-known result "the predual of Hardy space H1 is VMO" to the product setting, associated with differential operators. Let Li, i = 1, 2, be the infinitesimal generators of the analytic semigroups {e-tLi} on L2(ℝ).  Assume that the kernels of the semigroups {e-tLi} satisfy the Gaussian upper bounds.  We introduce the VMO spaces VMOL1,L2(ℝ × ℝ) associated with operators L1 and L2 on the product domain ℝ × ℝ, then show that the dual space of VMOL1,L2(ℝ × ℝ) is the Hardy space H1L1,L2 (ℝ × ℝ) associated with the adjoint operators L1 and L2.

    Original languageEnglish
    Pages (from-to)1065-1085
    Number of pages21
    JournalJournal of Geometric Analysis
    Volume27
    Issue number2
    Early online date26 May 2016
    DOIs
    Publication statusPublished - 2017

    Keywords

    • Hardy spaces
    • VMO spaces
    • Tent spaces
    • Product domains

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