Bloom Type Upper Bounds in the Product BMO Setting

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Abstract

We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral T n in R n and a bounded singular integral T m in R m we prove that ‖[Tn1,[b,Tm2]]‖Lp(μ)→Lp(λ)≲[μ]Ap,[λ]Ap‖b‖BMOprod(ν),where p∈ (1 , ∞) , μ, λ∈ A p and ν: = μ 1 / p λ - 1 / p is the Bloom weight. Here Tn1 is T n acting on the first variable, Tm2 is T m acting on the second variable, A p stands for the bi-parameter weights of R n × R m and BMO prod (ν) is a weighted product BMO space.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • Basque Center of Applied Mathematics
  • University of Helsinki
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Geometri

Nyckelord

Originalspråkengelska
TidskriftJournal of Geometric Analysis
StatusE-pub ahead of print - 2019 apr 18
PublikationskategoriForskning
Peer review utfördJa