Carleson Measure Characterization of Weighted BMO Associated with a Family of General Sets

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Abstract

In this paper, we introduce a weighted Carleson measure dνE , w associated with the family E, where E={Er(x)}r∈I,x∈X is a family of open subsets of a topological space X endowed with a nonnegative Borel measure μ satisfying certain basic conditions. Using Calderón–Zygmund theory, we show that the weighted BMO associated with the family E can be characterized by the weighted Carleson measure dνE , w.

Original languageEnglish
Pages (from-to)842-867
Number of pages26
JournalJournal of Geometric Analysis
Volume27
Issue number1
DOIs
StatePublished - 1 Jan 2017

Keywords

  • A weights
  • BMO
  • Calderón–Zygmund operator
  • Carleson measure
  • Hardy spaces
  • Maximal operator

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