Littlewood-Paley theory on metric spaces with non doubling measures and its applications

Chao Qiang Tan, Ji Li*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling measure satisfying a weak growth condition. Moreover, we prove that our setting mentioned above, is equivalent to the one introduced and studied by Hytönen (2010) in his remarkable framework, i.e., the geometrically doubling metric space with a non-doubling measure satisfying a so-called upper doubling condition. As an application, we obtain the T1 theorem in this more general setting. Moreover, the Gaussian measure is also discussed.

    Original languageEnglish
    Pages (from-to)983-1004
    Number of pages22
    JournalScience China Mathematics
    Volume58
    Issue number5
    DOIs
    Publication statusPublished - 1 May 2015

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