Browsing Harmonic Analysis by Title
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The observational limit of wave packets with noisy measurements
(2019)The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian ... 
On Bloom type estimates for iterated commutators of fractional integrals
(Indiana University Mathematics Journal, 201804)In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ... 
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 ... 
On pointwise and weighted estimates for commutators of CalderónZygmund operators
(Advances in Mathematics, 2017)In recent years, it has been well understood that a CalderónZygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... 
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(20160910)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... 
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 ... 
Proof of an extension of E. Sawyer's conjecture about weighted mixed weaktype estimates
(Mathematische Annalen, 201809)We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\\frac{ T(fv)} {v}\Big\_{L^{1,\infty}(uv)}\le c\, ... 
A quantitative approach to weighted Carleson condition
(Concrete Operators, 20170505)Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{Q}\int_{Q}f(x)dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ... 
Quantitative weighted estimates for rough homogeneous singular integrals
(Israel Journal of Mathematics, 20170311)We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ... 
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. ... 
Quantitative weighted estimates for singular integrals and commutators
(20180227)In this dissertation several quantitative weighted estimates for singular integral op erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, CoifmanFe ... 
Quantitative weighted mixed weaktype inequalities for classical operators
(Indiana University Mathematics Journal, 20160630)We improve on several mixed weak type inequalities both for the HardyLittlewood maximal function and for CalderónZygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ... 
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 ... 
Reverse Hölder Property for Strong Weights and General Measures
(Journal of Geometric Analysis, 20160630)We present dimensionfree reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ... 
Scattering with criticallysingular and δshell potentials
(2019)The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz ... 
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 ... 
Sharp weighted estimates involving one supremum
(Comptes Rendus Mathematique, 201707)In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ... 
Sparse and weighted estimates for generalized Hörmander operators and commutators
(Monatshefte für Mathematik, 2019)In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination ... 
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, ... 
Sparse domination theorem for multilinear singular integral operators with $L^{r}$Hörmander condition
(Michigan Mathematical Journal, 20170401)In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the socalled multilinear $L^{r}$Hörmander condition, then $T$ can be dominated by multilinear sparse operators.