Bloom Type Upper Bounds in the Product BMO Setting
We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral Tn 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