Browsing Harmonic Analysis by Title
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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 ... 
Mixed norm estimates for the Cesàro means associated with DunklHermite expansions
(Transactions of the American Mathematical Society, 2017)Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with DunklHermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the DunklHermite operator ... 
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(Colloquium Mathematicum, 20160101)In this paper we study mixed weighted weaktype inequal ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2]. 
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 ... 
New bounds for bilinear CalderónZygmund operators and applications
(Revista Matemática Iberoamericana, 20161125)In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... 
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
(Adv. Math., 2018)The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (\Delta_h)^su=f, \] for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ... 
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 ... 
A note on the offdiagonal MuckenhouptWheeden conjecture
(WSPC Proceedings, 20160701)We obtain the offdiagonal MuckenhouptWheeden conjecture for CalderónZygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the HardyLittlewood maximal function satisfies the following ... 
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 ...