Browsing Harmonic Analysis by Issue Date
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Multilinear singular integrals on noncommutative lp spaces
(Springer International Publishing, 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 ... 
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, 2019)Quantitative $A_1A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \T_\Omega ... 
Sparse bounds for maximal rough singular integrals via the Fourier transform
(Annales de l'institut Fourier, 20190312)We prove a quantified sparse bound for the maximal truncations of convolutiontype singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by CondeAlonso, Culiuc, ... 
Bloom type inequality for biparameter singular integrals: efficient proof and iterated commutators
(International Mathematics Research Notices, 20190314)Utilising some recent ideas from our bilinear biparameter theory, we give an efficient proof of a twoweight Bloom type inequality for iterated commutators of linear biparameter singular integrals. We prove that if $T$ ... 
On the absolute divergence of Fourier series in the infinite dimensional torus
(Colloquium Mathematicum, 20190322)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 upper bounds in the product BMO setting
(Journal of Geometric Analysis, 20190408)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, ... 
A Bilinear Strategy for Calderón's Problem
(201908)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
(201908)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 ... 
On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(Communications on pure and applied analysis, 201909)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 ... 
Bilinear CalderónZygmund theory on product spaces
(Journal des Math\'ematiques Pures et Appliqu\'ees, 201910)We develop a wide general theory of bilinear biparameter singular integrals $T$. This includes general Calder\'onZygmund type principles in the bilinear biparameter setting: easier bounds, like estimates in the Banach ... 
Análisis de Fourier en el toro infinitodimensional
(20191024)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 ... 
Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(Forum of Mathematics, Sigma, 201911)We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the JohnNirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ... 
Quantitative weighted estimates for Rubio de Francia's LittlewoodPaley square function
(Journal of Geometric Analysis, 201912)We consider the Rubio de Francia's LittlewoodPaley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. ... 
Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
(Annali de Matematica Pura et Applicata, 2020)We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ... 
A note on generalized Poincarétype inequalities with applications to weighted improved Poincarétype inequalities
(2020)The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent selfimproving result of generalized inequalities of Poincar\'etype in the Euclidean ... 
Sharp reverse Hölder inequality for Cp weights and applications
(Journal of Geometric Analysis, 2020)We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen ... 
A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the InfiniteDimensional Torus
(Potential Analysis, 20200213)In this note we will show a Calder\'onZygmund decomposition associated with a function $f\in L^1(\mathbb{T}^{\omega})$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting ... 
Topics in Harmonic Analysis; commutators and directional singular integrals
(20200301)This dissertation focuses on two main topics: commutators and maximal directional operators. Our first topic will also distinguish between two cases: commutators of singular integral operators and BMO functions and ... 
A Bilinear Strategy for Calderón’s Problem
(Revista Matemática Iberoamericana, 202005)Electrical Impedance Imaging would suffer a serious obstruction if two different conductivities yielded the same measurements of potential and current at the boundary. The Calderón’s problem is to decide whether the ...