Search
Now showing items 1-10 of 18
Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function
(2019-12)
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping.
Quantitative weighted estimates are obtained for this operator. ...
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 $A_\infty(\mathbb R)$ ...
Análisis de Fourier en el toro infinito-dimensional
(2019-10-24)
Se presentan algunos resultados originales de análisis armónico para funciones definidas en el toro infinito, que es el grupo topológico compacto consistente en el producto cartesiano de una familia numerable de toros ...
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 ...
On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(2019-09)
We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ...
A Bilinear Strategy for Calderón's Problem
(2019-08)
Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the ...
Reconstruction of the Derivative of the Conductivity at the Boundary
(2019-08)
We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness ...
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, ...
On the absolute divergence of Fourier series in the infinite dimensional torus
(2019-03-22)
In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication
$f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ...
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 $T$ ...