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Multilinear Calderón–Zygmund operators on the product of Lebesgue spaces with non-doubling measures

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
335
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2007.01.075
Keywords
  • Multilinear Calderón–Zygmund Operator
  • Lebesgue Space
  • Hardy Space
  • Non-Doubling Measure

Abstract

Abstract Under the assumption that μ is a non-doubling measure on R d , the author proves that for the multilinear Calderón–Zygmund operator, its boundedness from the product of Hardy space H 1 ( μ ) × H 1 ( μ ) into L 1 / 2 ( μ ) implies its boundedness from the product of Lebesgue spaces L p 1 ( μ ) × L p 2 ( μ ) into L p ( μ ) with 1 < p 1 , p 2 < ∞ and p satisfying 1 / p = 1 / p 1 + 1 / p 2 .

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