Some new weighted estimates on product spaces

Emil Airta, Kangwei Li, Henri Martikainen, Emil Vuorinen

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We complete our theory of weighted

L-p (w(1)) x L-q (w(2)) -> L-r (w(1)(r/p) w(2)(r/q))

estimates for bilinear bi-parameter Calderon-Zygmund operators under the assumption that w(1) is an element of A(p) and w(2 )is an element of A(q) are bi-parameter weights. This is done by lifting a previous restriction on the class of singular integrals by extending a classical result of Muckenhoupt and Wheeden regarding weighted BMO spaces to the product BMO setting. We use this extension of the Muckenhoupt-Wheeden result also to generalise some two-weight commutator estimates from biparameter to multi-parameter. This gives a fully satisfactory Bloom-type upper estimate for [T-1, [T-2, ...[b,T-k]]], where each T-i can be a completely general multi-parameter Calderon-Zygmund operator.
Original languageEnglish
JournalIndiana University Mathematics Journal
Volume71
Issue number1
Pages (from-to)37-63
Number of pages27
ISSN0022-2518
DOIs
Publication statusPublished - 2022
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics
  • Bilinear analysis
  • bi-parameter analysis
  • model operators
  • weighted estimates
  • SINGULAR-INTEGRALS
  • EXTRAPOLATION
  • REPRESENTATION
  • INEQUALITIES
  • OPERATORS
  • BMO

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