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Now showing items 1-10 of 19
RESTRICTED TESTING FOR POSITIVE OPERATORS
(2020)
We prove that for certain positive operators T, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant D>1, depending only on the dimension n, such that the two weight norm inequality ...
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 ...
Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(2019-11)
We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has
spatial derivative in the John-Nirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ...
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 ...
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, ...
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 $T$ ...
Sparse bounds for maximal rough singular integrals via the Fourier transform
(2019-03-12)
We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ...
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 ...
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. ...
Vector-valued operators, optimal weighted estimates and the $C_p$ condition
(2018-09)
In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...