Now showing items 1-7 of 7

• #### Bilinear Calderón--Zygmund theory on product spaces ﻿

(2019-10)
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach ...
• #### Bilinear representation theorem ﻿

(2018-01-01)
We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ...
• #### Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators ﻿

(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 $T$ ...
• #### Bloom type upper bounds in the product BMO setting ﻿

(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, ...
• #### End-point estimates, extrapolation for multilinear muckenhoupt classes, and applications ﻿

(2019)
In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. ...
• #### Multilinear operator-valued calderón-zygmund theory ﻿

(2020)
We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness ...
• #### Multilinear singular integrals on non-commutative lp spaces ﻿

(2019)
We prove Lp bounds for the extensions of standard multilinear Calderón- Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ...