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Bloom type upper bounds in the product BMO setting
(Journal of Geometric Analysis, 2019-04-08)
We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral $T_n$ in $\mathbb R^n$ and a bounded singular integral $T_m$ in $\mathbb R^m$ we prove that $$ \| [T_n^1, ...
Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators
(International Mathematics Research Notices, 2019-03-14)
Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ ...