Hardy and BMO spaces associated to divergence form elliptic operators

Steve Hofmann, Svitlana Mayboroda

Research output: Contribution to journalArticlepeer-review

151 Scopus citations

Abstract

Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy and BMO spaces, and a John-Nirenberg inequality.

Original languageEnglish (US)
Pages (from-to)37-116
Number of pages80
JournalMathematische Annalen
Volume344
Issue number1
DOIs
StatePublished - Feb 1 2009

Keywords

  • 35J15
  • 42B25
  • 42B30
  • 42B35

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