Atomic decomposition and boundedness of operators on weighted hardy spaces

Yongsheng Han, Ming Yi Lee, Chin Cheng Lin

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Abstract

In this article, we establish a new atomic decomposition for f ε L 2 w ∩ H p w , where the decomposition converges in L 2 w-norm rather than in the distribution sense. As applications of this decomposition, assuming that T is a linear operator bounded on L 2 w and 0 < p ≤ 1, we obtain (i) if T is uniformly bounded in L p w -norm for all w-p-atoms, then T can be extended to be bounded from HL p w to L p w ; (ii) if T is uniformly bounded in H p w -norm for all w-p-atoms, then T can be extended to be bounded on H p w ; (iii) if T is bounded on H p w , then T can be extended to be bounded from H p w to L p w.

Original languageEnglish
Pages (from-to)303-314
Number of pages12
JournalCanadian Mathematical Bulletin
Volume55
Issue number2
DOIs
StatePublished - 2012

Keywords

  • A weights
  • Atomic decomposition
  • Calderón reproducing formula
  • Weighted hardy spaces

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