Ap,E Weights, Maximal Operators, and Hardy Spaces Associated with a Family of General Sets

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Abstract

Suppose that 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. We establish an AE,p weights theory with respect to E and get the characterization of weighted weak type (1,1) and strong type (p,p), 1 < p ≤ ∞, for the maximal operator ME associated with E. As applications, we introduce the weighted atomic Hardy space H1E,w and its dual BMOE,w, and give a maximal function characterization of H1E,w. Our results generalize several well-known results.

Original languageEnglish
Pages (from-to)608-667
Number of pages60
JournalJournal of Fourier Analysis and Applications
Volume20
Issue number3
DOIs
StatePublished - Jun 2014

Keywords

  • BMO
  • Hardy spaces
  • maximal operator

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